The deadly surge happened at about 8 pm local time as thousands of passengers waited to board a train to the Maha Kumbh Hindu festival in Prayagraj in northern India.
Eyewitness Dharmender Singh said there was "a huge stampede... a huge crowd. I have never seen such a crowd before".
Those killed included 10 women and three children, according to Sky News.
Delhi's chief minister said on X that many of the victims were pilgrims en route to attend the Maha Kumbh festival.
Indian Prime Minister Narendra Modi and some other federal ministers confirmed the incident in posts on X, although they did not disclose the number of people who died.
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