The petrol bomb was thrown at the home in Clara Street at 11.35pm last night, Sunday, May 14.
The woman inside received injuries to her legs and was taken to hospital for treatment. Her injuries are not believed to be life threatening.
The house sustained smoke damage.
Detective Sergeant McPhillips would appeal to anyone who may have noticed any suspicious activity in the area to contact Detectives at Reactive and Organised Crime at Musgrave on the non-emergency number 101, quoting reference 1427 14/05/17.
“Alternatively, 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.”