At least six Kamayani Express coaches and four Janata Express coaches plunged into the river near the town of Harda in the state of Madhya Pradesh late on Tuesday, Sputnik reported.
The CNN-IBN broadcaster cited authorities as saying 12 bodies have been recovered so far. At least two of the dead were electrocuted during rescue efforts.
Among the dead were six men, four women and two children, according to the broadcaster.
Flooding on the train tracks due to heavy rains was blamed for the twin derailments.
The outlet cited a railway spokesman as saying the Machak River bridge that the trains were crossing was submerged under water.
The death toll is expected to rise as rescue operations are underway.