The alleged rapist was a 19-year-old fellow patient at the center in the capital, New Delhi, Parvinder Singh, an additional deputy commissioner of Delhi police, told CNN.
"The two did not know each other beforehand, the rape took place in an isolated area at the center and a 20-year-old man, a friend of the 19-year-old, assisted in the crime," Singh said.
The suspect and the alleged victim had tested positive for coronavirus and were patients at the 10,000-bed Sardar Patel Covid Care Centre in Chhatarpur, in the south of the city.
Police first registered the incident on July 16, when the girl's family reported the alleged attack.
"The girl alleged that the 20-year-old also recorded the rape on his phone. We are investigating this as well as the rape charge," Singh added.
The alleged incident has been registered as a case under the Protection of Children from Sexual Offenses (POCSO) act.
Singh told CNN that the two suspects have been arrested and are at a government hospital under judicial custody because they are being treated for coronavirus.
The girl is receiving treatment at a different government hospital, he added.
India has one of the highest coronavirus case counts in the world, with more than 1.28 million people infected with the virus, according to a Johns Hopkins University tally -- third only to the US, which has more than 4 million cases, and Brazil, with more than 2.28 million.
On Friday morning, India registered a new record high of 49,311 new virus cases recorded in 24 hours, according to the Ministry of Health and Family Welfare, and over the past two days, the country has seen a surge, recording just over 95,000 fresh cases.
But the numbers could be even higher in reality: A recent study by India's National Center for Disease Control found that nearly one in four residents in New Delhi may have been infected, suggesting actual infections in the city are more widespread than the number of confirmed cases.