Shortly after 6 am it was reported that a fire had been started in a flat in the area.
Police and NIFRS attended and the fire was extinguished.
While in attendance NIFRS discovered a fire in a second flat.
Damage was caused to both flats as a result of the incident.
Both flats were unoccupied at the time of the incident.
A female in an adjoining flat was treated for the effects of smoke inhalation.
Detective Inspector Denis McGaffin stated: “We are lucky not to be dealing with serious injuries or death as a result of this reckless action.
“A robust investigation has now commenced and I am appealing for anyone who witnessed the incidents or anyone with any information that can assist with the investigation to contact Detectives in Musgrave on 101 quoting reference 159 14/08/18.
“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.”