It happened in the seaside town of in Ballycastle, Co Antrim.
Police say flammable liquid was poured through the letter box of the property in Whitehill Avenue around 2.40 am.
North Antrim CID senior investigating officer, Det Ch Insp Catherine Magee said: “Extensive damage was caused to the front door of the property and smoke damage to the interior of the house.
“No-one was in the house at the time of the attack. I would appeal for anyone with information to contact us on the 101 non emergency number.
“Alternatively, information can be passed anonymously to Crimestoppers on 0800 555 111.”