Dr Megha Reddy, an anaesthetist from Wolverhampton, was on holiday with his family when the accident happened near the city of Hyderabad.
Dr Reddy, 42, said he took his 18-month-old daughter Manvi and her brothers, aged 10 and five, to see the Musi River, which was swollen from the heavy rains.
"I was holding Manvi when she suddenly moved and slipped from my arms," he told police. Reports said he was taking photos of her brothers when she fell.
Dr Reddy couldn't jump into the river because it was flowing so fast, police said, and passers-by were unable to rescue her.
Police inspector Srinivas Reddy said: "The sludge and swiftly flowing water deterred him from jumping into the river."
Police and swimmers also searched for her, but her body was found two days later three miles downstream by divers and a boat from India's National Disaster Response Force.
There was reportedly a 90-minute delay in the search while neighbouring police authorities argued over whose responsibility it was.
Police added: "The body was floating in the still water at the check dam. If there was any delay on our part in sending the boat, the body would have crossed the check dam."