The woman, in her early 20s and believed to be a tourist, was found stabbed in the neck and stomach. Her mobile phone, the knife used for the crime, and her sandals were found near the body.
Senior Superintendent of Police Rajesh Modak said the phone details will help trace the woman`s identity.
The body was later sent for post-mortem examination.
Police officials, who reached the tomb to investigate, said a person who had reportedly accompanied the woman to Agra, had probably murdered her and escaped without anyone noticing.