According to local media, the red-faced rhesus macaques snatched Covid-19 blood samples from four patients and fled the facilities near the Meerut Medical College in Delhi.
One of the monkeys was later spotted in a tree chewing one of the sample collection kits, the Times of India reported.
Dr S. K. Garg, a top official at the college, told Reuters: "Monkeys grabbed and fled with the blood samples of four Covid-19 patients who are undergoing treatment... we had to take their blood samples again."
He added: "No evidence has been found that monkeys can contract the infection."
The monkeys are said to be an increasing problem in urban areas of the country, but lockdown measures in the last two months have encouraged the monkeys.
Ragini Sharma, a home ministry employee, in 2018 told Sky News: "Very often they snatch food from people as they are walking, and sometimes they even tear files and documents by climbing in through the windows."
People have been told not to feed the monkeys during the pandemic as a preventative measure against spreading mutated versions from of Covid-19.
A senior biologist from the Tamil Nadu Forest Department previously warned the mutated virus could have a devastating impact on primate species and other wildlife which prey on them.
He told The Hindu: "The point is, we have very little understanding of the virus, and it is better to limit our interactions with wildlife till there is more research done on its effects on non-human primates and other animal species."