The trains were crossing a partially flooded bridge near Harda. Several coaches have fallen into a river below.
A railway spokesman has told the BBC that heavy rain had caused river levels to rise, submerging the track.
The Kamayani Express, on its way from Varanasi to Mumbai, derailed first while the Janata Express travelling in the opposite direction derailed shortly after.
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.
Railways Minister Suresh Prabhu tweeted: "Rushing emergency medical and other relief personnel to spot. Darkness, water creating hurdles but ordered all possible help. Trying our best."
He added that he had ordered an enquiry into the incident.
Prime Minister Narendra Modi has also expressed concern, and offered condolences to the relatives of those who died.