TEL AVIV—Israel is upping the vaccine ante, pressing citizens to get Covid-19 booster shots and saying those who don’t will face restrictions on traveling, dining out and other activities.

Holders of Israel’s vaccine passports must get a third dose of the Pfizer -BioNTech vaccine within six months of their second dose, or lose the so-called green pass that allows them more freedom.

“We are updating what it means to be vaccinated,” said Israel’s coronavirus czar, Salman Zarka, at a press conference Sunday unveiling the new policy.

A study released by the Israeli health ministry on Sunday found that within 12 days, recipients of a third shot were 10 times less likely to become severely ill and 11 times less likely to become infected than people who had received their second dose five months earlier.

Israeli health officials say they don’t know whether additional boosters, beyond the third dose, will be needed. But they are moving aggressively to get as many people as possible vaccinated with a third shot, as the more contagious Delta variant of the virus spreads. All Israelis over the age of 12 are now eligible to receive a booster if five months have passed since their second shot.

Other countries with widespread vaccination programs are expected to authorize booster shots in the coming months. U.S. regulators are likely to approve in mid-September a Covid-19 booster shot of those manufactured by Pfizer Inc. and partner BioNTech SE, Moderna Inc. and Johnson & Johnson, for vaccinated adults six months after their previous dose, rather than the eight-month gap previously announced, The Wall Street Journal reported Thursday.

After meeting with Israeli Prime Minister Naftali Bennett in the White House on Friday, President Biden said he would also consider lowering the timeline for Americans to five months after the second shot.

Pfizer and the two other companies whose vaccines have been authorized by U.S. federal regulators say booster shots are shown to increase protection against the risk of infection and illness from the coronavirus.

Wedding guests are required to present an app-based ‘green pass’ in Israel.

Photo: Nir Alon/Zuma Press

Israel’s green pass takes the form of code on a smartphone app or a printed certificate. It has been credited with helping to open up Israel’s economy after successive lockdowns.

People show it to gain access to restaurants, bars and other indoor public areas. On Monday, Israel’s government also decided that employees in the health, education, and social-welfare sectors must show green passes or a negative Covid-19 test to enter their workplaces.

Some business owners fear that the additional vaccination requirements could cause complications.

Roy Shadur, a 50-year-old restaurateur in the city of Ramat Gan, said that while he had received the third shot, the change to the vaccine-passport requirement could mean shutting his business because it comes without the formal government financial support involved in a mandated full closure.

His customers, he said, have dwindled as many families prefer to order in rather than get the required negative coronavirus test for their children, who aren’t yet eligible for a green pass.

“It’s just the part that hurts, without the medicine,” Mr. Shadur said, regarding the change to the green pass.

Covid-19’s Delta variant is proliferating world-wide threatening unvaccinated populations and economic recovery. WSJ breaks down events in key countries to explain why Delta spreads faster than previously detected strains. Composite: Sharon Shi The Wall Street Journal Interactive Edition

Other Israelis share the World Health Organization’s concerns that a shift among widely vaccinated nations to offer third booster shots could slow inoculation efforts in developing countries.

Bracha Arnold, a 33-year-old lawyer in Tel Aviv, said that she felt lucky to have access to a booster but that what she called hoarding of vaccines by rich countries was perpetuating the pandemic because unvaccinated countries would likely continue to create more variants of the virus.

“It’s a very unfair and unbalanced cycle,” she said.

Israel’s government considers the booster shots a necessity, with the country experiencing one of its worst Covid outbreaks despite 78% of Israelis aged 12 and over having received two shots of the Pfizer vaccine.

Authorities blame the surge on the fact that Delta is spreading at the same time that many people’s vaccinations are waning in effectiveness.

Israel’s seven-day average on Monday for confirmed Covid-19 cases was just over 1,000 per one million people, around double that of the U.S. and the U.K., according to Our World in Data, a project based at Oxford University.

Despite the scale of the outbreak, as of Aug. 29 Israel’s weekly hospitalizations per one million people were 155, while in the less-vaccinated U.S. they were 267, according to Our World in Data.

“The most vulnerable group right now are those people who have been inoculated with two doses and not the third,” Mr. Bennett said in a cabinet meeting last week, adding that they behaved as if they were fully protected, but weren’t.

Israeli Health Ministry data show that for most of the current outbreak, the majority of severely ill patients had previously had two doses of the vaccine. However, double-vaccinated people were still proportionately less likely to become severely ill than the much smaller group of unvaccinated patients.

In recent days, unvaccinated Israelis have made up the bulk of those severely ill—due in part, officials say, to a campaign to get people to take booster shots in August.

More than 2 million of Israel’s population of 9.3 million have already had a third shot, including 70% of Israelis aged 60 or over and nearly half of over 50s. Health officials said that data from the millions who have had the booster shots showed that side effects were similar to or less severe than those for the first two shots.

Officials now say that if at least one-third of the population gets the third booster shot, then Israel stands a better chance of emerging from its latest outbreak, the fourth wave of infections since the pandemic began.

As an extra inducement, the government is waiving a requirement for Israelis to quarantine for at least a week on their return from most countries if they have had a third shot, or less than five months have passed since their second.

Israeli healthcare providers say tens of thousands of younger people are scrambling to get booster shots. However, some are unhappy with the change to the green-pass requirement to include a third shot.

“Why are we the first country to do this,” said 28-year-old Tovatel Magen, who works at a cafe in Jerusalem and has had her first two shots. “They are doing experiments on us.”