Countries around the world reported their first cases of the Omicron variant over the weekend and some imposed new travel restrictions, racing to protect themselves against the potentially more contagious strain even as scientists cautioned they don’t yet know how severe it will prove to be.

Canada, Australia, the Netherlands and Austria on Sunday joined a group of countries that have detected a strain first documented in South Africa that authorities said could pose a greater risk of people falling ill with Covid-19 a second...

Countries around the world reported their first cases of the Omicron variant over the weekend and some imposed new travel restrictions, racing to protect themselves against the potentially more contagious strain even as scientists cautioned they don’t yet know how severe it will prove to be.

Canada, Australia, the Netherlands and Austria on Sunday joined a group of countries that have detected a strain first documented in South Africa that authorities said could pose a greater risk of people falling ill with Covid-19 a second time and could be more transmissible than other variants.

In a particularly tough move, Israel banned all foreigners from entry. Australia restricted some travelers from several African countries and the U.K. reintroduced mask mandates and PCR tests for travelers.

In the Netherlands, passengers traveling from South Africa were transported to a hotel for quarantine on Saturday.

Photo: laurens bosch/Shutterstock

Beginning Monday, the U.S. will ban entry of anyone present in South Africa, Zimbabwe and six other southern African nations over the previous two weeks.

U.S. health officials were working to prepare for the variant, which hasn’t been detected in the U.S. but which they said has likely already arrived. President Biden was briefed on the variant Sunday when he returned to the White House from his Thanksgiving break. He is to provide an update about Omicron and the U.S. response to it on Monday, the White House said.

While new travel restrictions show how seriously authorities in nations around the globe are taking the new variant, scientists and health experts warned that very little is known about Omicron. On Friday, stocks and government-bond yields slumped after South Africa sounded the alarm about the new strain, raising concern that new restrictions could endanger the global economy’s recovery.

Dr. Anthony Fauci, the Biden administration’s chief medical adviser, said on NBC on Sunday that the Omicron variant is raising concern among scientists because it carries at least 30 mutations on the virus’s spike protein, the mechanism it uses to bind to human cells, that suggest it could spread even faster than the Delta variant.

Mr. Fauci said the series of travel bans would buy the U.S. time to prepare for Omicron.

“When you diminish or stop travel from a particular country, there’s a reason for that,” he said. “It gives you time.”

Biden administration officials don’t expect to know for about two weeks whether the new variant increases the severity of cases, the White House said after the Covid-19 response team briefed the president. South Africa is seeing a small increase in the number of breakthrough cases with Omicron among vaccinated people, a person familiar with the matter said.

The administration is in discussions with South African scientists, vaccine manufacturers, and academic labs to adapt vaccines and therapeutics, if they are needed, the person said.

After detecting one case of the new strain on Friday, Israel banned all foreign nationals from entering the country on Sunday and reinstated a controversial contact-tracing surveillance program. Israel’s health ministry also said Israelis would be prohibited from traveling to 50 African countries.

New regulations will require Israelis returning from abroad to quarantine for at least three days, among other measures.

Photo: abir sultan/Shutterstock

Along with new travel restrictions, Israel’s cabinet voted to allow the country’s internal security service, the Shin Bet, to renew the use of contact tracing through cellular location services for cases related to the Omicron variant. Israeli civil- and human-rights groups have condemned the involvement of the Shin Bet, whose mandate is to fight terrorism, as a violation of privacy.

Canada reported its first cases, involving two individuals in the capital, Ottawa, who had recently traveled to Nigeria. The two are in isolation. Canada on Friday said it was prohibiting entry into the country by foreign nationals who were in southern Africa during the past 14 days.

Dutch health authorities said Sunday they had confirmed 13 cases of the new variant among 61 positive Covid-19 tests from passengers on two flights that arrived in the Netherlands from South Africa on Friday. It was possible that further sequencing would find more cases of Omicron, they said.

If scientists confirm early indications that Omicron is more transmissible than the Delta variant and is better able to infect people a second time, it raises new questions on how societies will manage to live with Covid-19 in the long term.

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“How much more can society take?” asked Simon Quijano-Evans, chief economist at Gemcorp Capital LLP in London, in an email to clients Saturday, without answering the question.

In the U.K., which has tolerated relatively high numbers of Covid-19 cases since the summer largely without reimposing restrictions, the government on Saturday said it would once again require masks in shops and on public transportation and require anyone entering the country to isolate until a PCR test shows a negative result.

Since the summer, a number of European Union countries had gained some measure of control over the virus by retaining mask mandates and deploying measures—such as vaccine requirements for recreation and even to enter the workplace—aimed at pressuring people to get the shot.

In the U.K., the government said Saturday it would reimpose mask mandates in shops and on public transportation.

Photo: Matt Dunham/Associated Press

But even before Omicron emerged, a surge in the EU in cases, which have overtaken the U.S. on a per capita basis, had shaken policy makers’ confidence, pushing some authorities to reimpose lockdowns and curfews and make vaccines obligatory for virtually everyone.

On Saturday, the Australian government tightened border restrictions, barring those who aren’t Australian citizens, permanent residents or their immediate family from entering the country if they have been in several African countries within the past 14 days. Those countries include South Africa, Namibia, Zimbabwe and Botswana.

Australia in November reopened its international border, ending one of the world’s strictest pandemic-era travel bans as authorities pivot from trying to suppress Covid-19 to living with it.

Meanwhile, Omicron could cause Asian countries that have pursued zero-tolerance policies to reconsider recent, tentative reopening plans.

Last week, China’s Centre for Disease Control and Prevention published a report saying that the country could face more than 630,000 Covid-19 infections a day if it dropped its ultrastrict containment measures, including travel curbs, and adopted pandemic measures followed by the U.S. and other Western countries.

Researchers used data from August from the U.S., the U.K., France, Israel and Spain to assess the impact on China if it adopted the same pandemic policies as those countries.

It said that it could see more than 10,000 severe cases a day, potentially exerting “a devastating impact on the medical system of China and cause a great disaster within the nation.”

—Michelle Hackman, Stephanie Armour, Georgi Kantchev and Alice Uribe contributed to this article.

Write to Kate O’Keeffe at kathryn.okeeffe@wsj.com