Officials said that a technician reused a tube used to treat an individual with HIV on other patients.
Provincial authorities described it as a "severe violation of procedure".
Five people had been sacked at Hangzhou's Zhejiang Provincial Hospital of Chinese Medicine, they said.
Provincial health officials said they were informed of the situation on 26 January.
But in a statement (in Chinese) they gave no information on how many other patients might have been exposed, what they were being treated for or when the infections occurred.
Those affected would receive treatment and compensation, the brief statement said.
Two decades ago low safety standards and insufficient regulation helped spread HIV/Aids in China, and the news of the hospital incident sparked shock and criticism from social media users.
"A provincial-level hospital doesn't follow protocols, who can we trust as average citizens?!", wrote one person on Weibo, China's version of Twitter.
"This case is exposed, but what about cases that we don't know? There must have been many more!" wrote another.
Cases of HIV/Aids rose sharply in China after a major scandal in Henan province in the 1990s, when farmers who sold their blood contracted HIV through poor safety practices.
Donors' collected blood was pooled together and the lucrative plasma removed. The remaining blood, now cross-contaminated, was then injected back into the donors so they could donate again soon.
For years officials tried to cover up the problem and it is still not clear how many were infected. China said in 2001 that between 30,000 and 50,000 people had contracted HIV through the blood-selling scandal, but other officials have since suggested the figure was much higher.
The scandal did help highlight the ways in which HIV could be passed, and rules surrounding blood donation and transfusions have since improved, but illegal practises remain.
In 2006, a group of 19 people sued a hospital in Heilongjiang over transfusions from which they contracted HIV.
In a recent report, China said it had 501,000 reported cases of HIV/Aids by the end of 2014. It gave no estimate of unreported cases.