Police say a window was broken at the property at Cloona Manor in Dunmurry just before 12.45 am.
A device was thene thrown at the front door, causing minor damage.
No-one is believed to have been in the property at the time of the incident.
A second unexploded petrol bomb was found in the driveway of the house.
It has been taken away for forensic examination at the Northern Ireland Forensic Science laboratory.
Detectives in west Belfast have appealed for anyone with information to contact them on the 101 non-emergency number.