Senior superintendent Subhah Chandra Dubey told the BBC the hotel owner claimed to have knocked on the tourist's door after staff failed to rouse her on the intercom.
Mr Dubey said the woman was moved to another hotel and allocated two female constables as security following her ordeal.
A Foreign Office spokesman said: "We are aware of an incident involving a British national in Agra, India. We are in contact in with the local authorities and are providing consular assistance to the British national."
The episode comes days after a Swiss woman was gang raped while cycling through a neighbouring state with her husband.
The woman was attacked on Friday night when the couple stopped to camp in a forest in the Datia district of Madhya Pradesh, 120 miles south of Agra.