State minister Azam Khan said he was "stepping down on moral grounds".
The victims were among about 30 million Hindu pilgrims returning home after the main bathing day at the gathering.
Earlier, India's railway minister said the stampede had been caused by too many people being on the platforms.
At least 39 others were injured in the stampede on Sunday evening. Most of the victims were women and children.
Sunday was the most auspicious of six bathing days at the Kumbh Mela, which is billed as the world's biggest human gathering.
The festival, which is held every 12 years, expects 100 million bathers in total across its 55 days.
The present festival is also a Maha Kumbh Mela, which comes round only once every 144 years.
Hindus believe a festival dip at Sangam - at the confluence of the Ganges, Yamuna and mythical Saraswati rivers - will cleanse sins and help bring salvation