The two-storey house in Crossmaglen, which was near completion, is owned by Crossmaglen Rangers player Danny O'Callaghan.
The police are appealing for information.
They want to hear from anyone who was in the Monog Road area between midnight and 02:15 BST on Sunday.
A fire that destroyed a house being built by a well-known GAA footballer in south Armagh is being treated as arson.