Forty others were injured when the makeshift tent caved in following strong winds at one of the sites of the Kumbh, a pilgrimage that draws millions over four weeks to participate in a sacred bathing ritual.
"We have recovered seven bodies and 40 people are injured," Rakesh Gupta, a senior regional police officer in Madhya Pradesh state, told AFP, adding that emergency workers in Ujjain district took the injured to hospital.
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The officer said the tent's collapse triggered a minor stampede but could not confirm whether any of the deaths were caused by the crush. Fatal stampedes at religious gathering are common in India.
India's premier offered his condolences to the families of the victims on Twitter.
"Anguished over the loss of lives at the Kumbh due to heavy rains. May Almighty give strength to the bereaved families to overcome the grief," Prime Minister Narendra Modi tweeted.
The month-long Simhastha Kumbh Mela, which began on April 22, is the largest Hindu event to take place on the banks of the river Kshipra, with about 50 million pilgrims expected to attend.
The event is held every 12 years in accordance with the celestial line-up of planets.
In 2013, more than 100 devotees were killed in a stampede at a temple in Madhya Pradesh state.
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