The accident occured near Badarwas station, about 260 km (160 miles) north of Bhopal, the state capital.
"We have recovered 20 bodies so far and rescue operations are still on," said Raj Kumar Pathak, a senior government official.
Local villagers joined authorities and rescued several passengers trapped inside the damaged compartments, witnesses said.
Some of the critically injured were taken to a hospital on a helicopter, officials said.
Railway authorities ordered a probe to determine how both trains ended up in the same track.
In July, at least 60 people were killed in eastern India after one train crashed into another waiting at a station in eastern West Bengal state.
With a 63,327-km (39,350-mile) network, the railways play a key role, transporting more than 18 million passengers and more than 2 million tons of freight daily.
But the system is plagued by overcrowding and outdated technology, such as signaling systems. (Reuters)
