The attack happened at a house in the Queens Park area of Ballymena, Co Antrim.
Around 11 pm, an accelerant was poured through the letter box of a house and set on fire.
No one was in the house at the time of the incident.
Detective Chief Inspector James Mullan, Reactive and Organised Crime said: “I would appeal to anyone with any information about this incident or saw anyone acting suspiciously in the area around 11 pm to contact detectives at Ballymena on the non emergency number 101.
“Or if someone would prefer to provide information without giving their details, they can contact the independent charity Crimestoppers and speak to them anonymously on 0800 555 111.”