The university said staff are assisting the police in every possible way in looking at a "support department".
An internal inquiry has also been ordered by the university.
Police Scotland confirmed the investigation is under way, and that it involves a former employee of the university.
A statement from the university said: "The University of Edinburgh alerted the police to an issue relating to potential financial irregularities within a support department.
"This is now the subject of an internal inquiry at the University and a Police Scotland investigation.
"The university will be assisting the police in every way possible with their inquiries. It would not be appropriate to comment further at this time."
A Police Scotland spokesman said: "We have received a complaint regarding concerns over the management of finances at Edinburgh University by a former employee.
"The Economic Crime Unit has a positive line of inquiry and while our investigation is ongoing it would be inappropriate to comment further at this time."
Officers from Police Scotland have started an investigation into apparent financial irregularities at Edinburgh University.