Police were called to the property in Thornhill Road at about 11:00 on Saturday following the discovery of the body.
The death is being treated as unexplained and a post-mortem examination will be held to establish the cause.
A Police Scotland spokesman said a disturbance had earlier been heard in the block of flats.
Forensic examinations are taking place at the scene and there is an increased police presence in the area.
Officers are appealing for any witnesses who may have been in the Thornhill Road area between 17:00 on Friday and 11:00 on Saturday to come forward.
Det Ch Insp Jim Smith said:  "This is a heartbreaking time for the deceased's family and they are being supported by officers at this time.
"We are aware that sounds of a disturbance were heard within a block of flats in Thornhill Road and are keen to hear from anyone who was in that area during the evening of Friday 10th April and into the early hours of Saturday 11th April.
"Anyone who saw or heard anything that was out of the ordinary is asked to contact Police Scotland immediately."
The body of a 30-year-old man has been found at a flat in Falkirk.