The incident happened in Summerhill Road in the Drumchapel area of Glasgow last week.
No-one was injured and it is understood police are treating it as a targeted incident.
A Police Scotland spokesman said: "Around 6am on Friday December 6, police received a report that shots had been fired in the early hours of Thursday morning at a house in Summerhill Road, Drumchapel.
"No-one was injured and enquiries are ongoing to establish the exact circumstances and trace who is responsible."
Officers are carrying out extra patrols in the area to reassure the public.
Anyone with information is asked to contact the force on the non-emergency number 101 or Crimestoppers anonymously on 0800 555 111.