The officer and a colleague were called to a disturbance in Cardigan Road, Hyde Park, at about 04:00 GMT.
They were confronted by a man at the property and a gun was fired, police said. The female officer's injuries are not believed to be life-threatening.
Police said they want to speak to 37-year-old James Leslie, of Cardigan Road, in connection with the shooting.
Mr Leslie was last seen on a bike heading away from Cardigan Road towards Victoria Road, officers said.
Assistant Chief Constable Geoff Dodd said: “The police are actively seeking Mr Leslie and the public should be reassured that every effort is being made to safely locate him.
“Additional patrols will be seen in the area. The public should not approach Mr Leslie but ring 999, if they see him or know where he may be.”
The injured officer's male colleague was not hurt in the shooting.