The trains were crossing a partially flooded bridge near Harda and several coaches have fallen into a river.
A railway spokesman told the BBC that heavy rain had caused river levels to rise, submerging the track.
Officials are saying at least 25 people are injured and 300 people have been rescued.
The Kamayani Express travelling from Varanasi to Mumbai derailed first, while the Janata Express travelling in the opposite direction derailed shortly after.
Several coaches were submerged in the river
At least 25 people have been injured and 300 have been rescued
The Press Trust of India reported that it was not clear how many passengers the trains had been carrying.
Reports say the trains were crossing a bridge over a rain-swollen Machak river, about 950km (590 miles) from India’s capital, Delhi.
“This unfortunate accident took place because of the flash floods on the tracks and the track caved in and resulted in the derailment of the last six coaches of the Kamayani Express,” railways spokesperson Anil Saksena told the BBC.
“This train derailed, then simultaneously on the neighbouring line from the opposite direction, another train was coming. That train also encountered a flash flood situation. So it almost happened simultaneously on neighbouring tracks.”
Mr Saksena said at least two coaches had been partially submerged in the river and most passengers had been pulled to safety. But officials say dozens have been taken to hospital.
Railways Minister Suresh Prabhu tweeted that he had ordered an inquiry into the incident and that he would make a full statement to the Indian parliament later on Wednesday.
Prime Minister Narendra Modi has also expressed concern, and offered condolences to the relatives of those who died.
Safety standards on India’s massive state-run railway network, which operates 12,000 passenger trains and carries some 23 million passengers every day, has been an ongoing concern amid a spate of accidents.
Last March a passenger train derailed in the northern state of Uttar Pradesh, killing at least 34 people.
And in February last year, at least 11 people died after three coaches of the Bangalore-Ernakulam Intercity Express derailed in the southern state of Karnataka.
Correspondents say the state-run railway network has a patchy safety record – there has been little investment in upgrading decaying tracks and signals and the country lags behind on anti-collision technologies.
Decades of neglect, low investment and subsidised fares have left the network in a shambles.