BEIJING—China will punish 357 officials implicated in the sale of improperly handled vaccines, a scandal that has reignited drug safety fears and further eroded trust in the country’s public health system.

Officials found to have been involved will be fired or demoted, and criminal charges may be filed against some of them, the government’s state-controlled news agency, Xinhua, said Thursday, citing an announcement from China’s cabinet, the State Council.

As of Monday, authorities had filed 192 criminal cases and detained 202 people connected with the scandal, Xinhua said.

The vaccine scandal is the latest to hit a public health system that the government has struggled to reform to provide better and more affordable care. While vaccines for polio, measles and some infectious diseases are distributed free, those to prevent rabies, flu and some other diseases are sold and, experts said, the distribution and sale of these vaccines have proved problematic to monitor for quality.

The State Food and Drug Administration announced in March that it identified nine drug wholesalers involved in the alleged reselling of vaccines that had been stored and transported without proper refrigeration. Grass-roots health clinics run by local governments purchased the vaccinations, according to Xinhua.