It isn’t just Ukrainians who are fleeing. Russians are leaving their homeland too.

One man, worried he might soon be unable to buy insulin for his wife, loaded two suitcases with medicine, two more with clothes and left with his spouse to stay with their daughter in Germany.

Another left as soon as he had buried his mother, seeking to settle in Israel, saying he felt suffocated by war propaganda. A woman who was arrested at an antiwar march swiftly gathered her things and flew to Armenia with her young son

One Russian who entered Finland on Monday said that after his train crossed the border, a passenger near him shouted “Glory to Ukraine!”

Harsh sanctions, growing isolation and fear of President Vladimir Putin’s increasingly repressive rule are driving thousands of Russians out of their country. While the numbers pale compared with the two million who have fled Ukraine, they could be the front edge of a wave of people leaving due to shrinking political freedom and economic hardship. Many of those leaving are professionals and well-to-do Russians, along with journalists, activists and cultural figures.

“My father said, ‘Leave, leave, leave, you can get stuck here’,” Julia Zakharova, a 36-year-old employee of an American company said Tuesday minutes after crossing the Finnish border with Russia. For years, she and her Greek husband, a chief executive of a tech startup, have been commuting by plane between Russia and Greece, but they have now decided to relocate for the foreseeable future to Greece, partly because she was seven months pregnant.

“I’m not going to give birth in Russia when the perspective is like this,” Ms. Zakharova said.

Precise data on how many Russian nationals have left in recent weeks wasn’t available, and it isn’t clear that everyone who crosses a border will stay away long term. However, data shared by different countries suggests the figure is in the thousands.

About 44,000 people crossed the Russian border into Finland in February, up from some 27,000 in the same month last year, according to the Finnish Border Guard. Bus and train tickets to Finland are sold out, and Finland’s state-owned rail operator VR has said it would try to add more trains to its Helsinki-St. Petersburg connection.

Some have left Russia for countries such as Turkey, Georgia, and Armenia, which offer Russians visa-free entry or have relaxed entry requirements

Georgia’s economy minister has said that between 20,000 and 25,000 Russians entered the country in recent days. Israel has issued 1,400 immigrant visas to Russians since the invasion of Ukraine, Neta Briskin-Peleg, an immigration official, was quoted as saying in the Israeli daily Haaretz on Tuesday.

The opportunities to leave Russia are rapidly narrowing. Russia has reciprocated airspace bans restricting access to airlines including those from the European Union, the U.K. and Canada. Following sanctions targeting Russia’s aviation sector, leased Russian planes were impounded at airports outside the country. Major Russian airlines have halted international flights, while Moscow’s flag carrier Aeroflot halted all flights abroad except to Belarus.

Some Russians fear that Mr. Putin may soon declare martial law, which would enable him to further expand censorship and shut the borders. Mr. Putin said Saturday there was no need to declare martial law.

An actress and director from St. Petersburg who was arrested at an antiwar protest a few days after Russia’s invasion, rushed to buy plane tickets to Armenia for herself and her 5-year-old son after she was released.

She said she waited at the airport for 16 hours for a flight packed with Russian families. Once in Yerevan, she learned that a police officer had visited her address in St. Petersburg. She is worried about going back to Russia but said she only has enough money to get by in the Armenian capital for one or two months.

I don’t know what I’ll do,” she said.

Mr. Putin has long sought to silence critics, but pressure mounted last week when the Russian Parliament passed a law imposing jail terms of up to 15 years in jail for intentionally spreading “fake” information about the military.

“We are forbidden from even calling it a war,” said Evan Sergeyev, who was traveling with his wife and their 5-year-old son to Barcelona to stay with friends for an indefinite period. Mr. Putin said his invasion of Ukraine is a “special operation.”

On the messaging app Telegram, Russians swap logistical details on visa procurements and Covid-19 test requirements and the availability of tickets.

The exodus of educated, liberal Russians threatens the country’s long-term development in a brain drain that wouldn’t be Russia’s first. When the Soviet Union opened the door to greater Jewish emigration in the 1970s, many scientists, engineers, and doctors left for Israel and the West.

After the torrent of Western sanctions-hit Russia recently in response to Mr. Putin’s invasion of Ukraine, a Russian man in his 50s who said he worked for a U.S. company watched anxiously as medicine disappeared off the shelves in Moscow. He managed to find a pharmacy that still stocked insulin, packed as much as he could carry, and took the train to Helsinki with his wife, from where they planned to fly to Germany to move in with their daughter, a student.

“We decided that if we missed this opportunity, it would be too late,” he said as he waited in Helsinki airport.