The man, who was in his 40s, was found in a residence on Academy Street in Navan.
His body remains at the scene, which is preserved for forensic and technical examination by the Garda Technical Bureau.
The Office of the State Pathologist and local coroner have been notified.
The woman being held at Kells Garda Station.
Gardaí are appealing for witnesses to come forward. Anyone with information is asked to contact the incident room at Navan Garda Station 046-9036100 or the Garda Confidential Line 1800 666 111.