Officers on patrol were called to South Leith Parish Church at about 5:30pm.
An local resident described seeing one police car and a police van at the scene, with tape at both gates and an officer standing guard at the east entrance.
The police spokesman said: "At about 5:30pm, officers on patrol in Edinburgh were alerted to a woman in distress in the New Kirkgate area.
"Inquiries are ongoing in the area to establish the circumstances and whether any crime has taken place."
The spokesman was unable to provide any more details about the nature of the incident at this stage.
The spokesman confirmed that the incident took place within the church grounds and that, contrary to some local reports, a body has not been found there.