The corpse was found by police who forced entry to the flat in Finedon, Northamptonshire, after the housing association called them.
A spokeswoman for Wellingborough Homes said the neighbour had called to report the maggots and they had sent out a housing officer.
She said staff were notified by the neighbour who was concerned about an elderly tenant who had not been seen for some time.
The spokeswoman said: "In response the police were called and asked to gain entry, whereupon the occupant was found to be deceased. The Coroner's Office was informed.
"The flat, and those in the same block, required specialist cleaning and this was completed today.
"At this time we must also pass on our condolences to any friends or family of the deceased."
Neighbour Trevor Cutler, 68, who lives below the first-floor flat, told the Northamptonshire Evening Telegraph he had heard something falling from his ceiling on Tuesday night but did not know what it was.
He told the newspaper: "Then on Wednesday, when I was sitting watching television, I heard it again.
"I went over to the corner of my room and noticed maggots over the stereo, on the unit and on the floor.
"They were coming from the ceiling and dropping down."
He said he had not seen his elderly neighbour for about two weeks, and had previously seen him walking about the area.
A Northamptonshire Police spokeswoman confirmed they had been alerted by a member of the public to a man's body at the address.
She said the death was not being treated as suspicious and they were preparing a file for the coroner.
This is the stuff of nightmares.
I am now terrified of my ceiling collapsing beneath the weight of maggots.