Doctors at the Rajawadi hospital stated to foreign media that she was "doing fine" and her health was being monitored.
Police said residents found the baby after a group of cats gathered at a spot along the road and began creating a ruckus - hissing, and purring loudly.
Officials are investigating how she ended up in the drain.
Police have not speculated on possible motives, but similar abandonments in the past have been blamed on India's preference for sons. Women are often discriminated against socially and girls are seen as a financial burden, particularly among poor communities.
The country's gender ratio is one of the worst in the world. And although most unwanted female foetuses are aborted with help from illegal sex determination clinics, cases of baby girls being killed or abandoned after birth are not uncommon either.
In the latest incident, the baby was rescued by a women-led police team from a suburban Mumbai neighbourhood on Sunday.
When the police arrived, they found the infant lying inside the drain. They said the baby - dressed in a flimsy shirt and soaked in sewage water - was wailing in distress.
Two officers then scooped her out, wrapped her in a cloth and took her to the hospital.
"When we lifted the baby out, she was freezing; her arms had turned blue. We asked for some warm water and cloth to clean the baby," police constable Sheetal Sonawane told The Times of India newspaper.
Doctors at the Rajawadi hospital said the baby was "stable".
Pantnagar P.stn received a call from a good samaritan that a baby, wrapped in cloth, was dumped in a drain. He was alerted when the neighbourhood cats created a ruckus. the baby was rushed to Rajawadi by the Nirbhaya Squad of Pantnagar P.Stn & is now safe & recovering. pic.twitter.com/nEGSDCD6wz
— Mumbai Police (@MumbaiPolice) November 15, 2021