The family living in the property in Muirhouse Green have been moved to alternative accommodation and patrols have been increased in the area.
A forensic examination was carried out in the area, which led police to believe that a shotgun had been fired at a door of the house.
No-one was injured in the incident, which took place at about 0300 BST.
A police spokeswoman said a mother and her adult son were in the house at the time of the shooting.
"We are keen to hear from people living in the vicinity of Muirhouse Green or anyone who was in the area at around 0300 BST this morning and who may have seen or heard anything suspicious.
"We would also like to speak to anyone who may have information about the culprit.
"While police enquiries continue there will be increased patrols in the area."
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