SINGAPORE—At least 10 of the 26 doctors in Indonesia who died from Covid-19 this month had received both doses of the vaccine developed by Sinovac Biotech Ltd., a medical association said, raising questions about the Chinese-made shot that is being used in many parts of the developing world.

The Indonesian Medical Association’s Covid-19 mitigation group is still working to verify the vaccination status of the 16 others, said Dr. Adib Khumaidi, who leads the group. According to the group’s latest figures, over a five-month period, at least 20 doctors who were fully inoculated with Sinovac’s vaccine died from Covid-19, accounting for more than a fifth of total fatalities among doctors during that time span.

The toll could rise further in the coming weeks as the country battles a surge in infections and hospitals across the archipelago fill up.

Epidemiologists say the deaths need to be properly investigated to determine whether factors such as poor hospital care or chronic underlying illnesses played a major role. They also say more data is needed, including on how many vaccinated doctors overall were infected with Covid-19, which Indonesia’s health ministry says it isn’t tracking.

Around 90% of Indonesian doctors—roughly 160,000 in all—have been vaccinated with Sinovac’s shot, according to the medical association, so the vaccinated doctors who died are only a tiny percentage of the total.

That some fully vaccinated Indonesian doctors died from Covid-19 isn’t necessarily surprising, said Paul Hunter, a professor of medicine at the University of East Anglia in the U.K. A combination of factors was likely at play, he said, including that the Sinovac vaccine was “probably not as effective a vaccine as most of the other vaccines that are on the market” and Indonesian hospitals don’t always have the same machinery and capacity to handle severe cases as hospitals in countries with stronger healthcare systems.

Indonesia is relying heavily on the Sinovac vaccine. The shot is approved by the World Health Organization for emergency use, but wide-ranging efficacy levels from different clinical trials and a lack of transparency about the data have led to concerns among some public-health experts about the degree of protection it provides as well as how long the protection lasts.

Its efficacy in preventing symptomatic infections was as low as around 50% in a study from Brazil, though the vaccine has shown higher efficacy in preventing severe Covid-19 cases. Authorities in Chile said in April the shot was 80% effective against death from Covid-19 two weeks after a second dose.

Indonesian authorities said last month that a retrospective study comparing how vaccinated and unvaccinated doctors in the capital, Jakarta, had fared against Covid-19 showed Sinovac’s shot was highly effective in preventing death. The study was conducted before the current wave of infections, which is being driven in part by the highly transmissible Delta variant of the virus, which contributed to a devastating surge in India. It isn’t known how many doctors who died in Indonesia this month were infected with that strain.

A government spokeswoman said the individual circumstances of the doctors’ deaths needed to be investigated to draw conclusions about the vaccine. In some hard-hit areas of the country, such as Kudus in central Java, most of the several hundred vaccinated health workers who were infected with Covid-19 had mild symptoms and made quick recoveries, the spokeswoman, Siti Nadia Tarmizi, said. “It really can’t be said that Sinovac isn’t ideal,” she said.

Data gathered by the medical association shows the death toll among doctors is down from the country’s last surge in December and January, when vaccinations had just begun and around 60 doctors died in each of the two months from Covid-19. So far in June, 26 doctors have died.

In Surabaya, a large city in East Java province, a 54-year old radiologist named Eko Sonny Tejolaksito died from the disease in early June. He had been fully vaccinated with Sinovac’s shot earlier in the year, said Dr. Catur Budi Keswardiono, a close friend of his who worked with him at a hospital in a neighboring town. Dr. Eko had high blood pressure and diabetes, Dr. Catur said, making him more vulnerable to complications from Covid-19.

When Dr. Eko tested positive for the illness, his condition wasn’t especially severe and he sought treatment at a local hospital that didn’t have an intensive-care unit. His health deteriorated quickly over the next two days, however, and preparations were made to shift him to a ventilator-equipped hospital, Dr. Catur said. Dr. Eko died before he could be moved.

The deaths should prompt authorities to consider booster shots, said Jin Dong-Yan, a professor of molecular virology at the University of Hong Kong. Medical workers in Indonesia should be given another dose of Sinovac’s vaccine or of a U.S.-developed shot to ensure stronger protection, he said. Dr. Adib of the Indonesian Medical Association’s Covid-19 mitigation unit also said booster shots may be necessary, adding: “We don’t know how long the antibodies last.”

Write to Jon Emont at jonathan.emont@wsj.com