Hundreds of thousands of people lined the river before dawn on Saturday at Ganga Sagar where it empties into the Bay of Bengal, 75 miles from Kolkata, the capital of West Bengal.
However, an official said four people died and two dozen more fell ill after entering the chilly Ganges, which Hindus worship as a goddess.
Roshni Sen, a district magistrate, said: "Four people have died because of cold." Sen said that the victims were old people who had succumbed to the early-morning chill and exhaustion.
End of winter
The religious festival of Makar Sankranti (Capricorn transition) is celebrated when the Sun enters a new zodiac sign, marking the end of winter and the beginning of the harvest season.
The massed faithful offered prayers to Kapil Muni, the god who is said to have brought the Ganges to the Earth.
Winter temperatures have plunged to 70-year lows, leaving nearly 200 people dead in India.