A report of a fire at the house in the Parkanaur Road area of Dungannon was received by police at around 12.30 am.
The house, which has been completely destroyed as a result of the fire, was unoccupied at the time.
Sergeant McKinley said: “Whilst our enquiries at an early stage, we do believe at this time that the fire was started deliberately.
“I would therefore appeal to anyone who witnessed any suspicious activity in the Parkanaur Road area at the time of the incident or who has any information which could assist us with our investigation, to contact police in Dungannon on 101 quoting reference number 33 03/05/18.
“Alternatively, information can also be provided to the independent charity Crimestoppers on 0800 555 111 which is 100% anonymous and gives people the power to speak up and stop crime.”