The incident happened at a village near Datia where the woman and her husband were camping. They had halted there while on their way from Orchha to Agra. They had planned to cover the 250-km stretch on bicycles.
According to the woman's husband, around 9:30 at night, a group of seven men with lathis in their hands overpowered him, and then four of them gang-raped his wife. The men also beat him up, he said.
The woman was taken to a hospital in Gwalior where her medical examination confirmed that she was gang-raped.
Based on her husband's complaint, police in Datia have detained 20 men. The couple will now be asked to identify the accused.
"Twenty people have already been detained on the basis of suspicion and are being questioned in connection with the incident," Deputy Inspector General (Chambal range) DK Arya said.