Police said that a car entered Flynn Gardens in Stepps and two shots were aimed in the direction of the property, at about 6:50pm on Monday December 30th.
No one was injured during the attack.
Officers are now carrying out door-to-door inquiries in the area and reviewing CCTV footage.
Detective Inspector Kenny Dalrymple, the officer in charge of the enquiry, is appealing for anyone who has information about who was responsible to come forward.
He said: "The information we have at this time leads me to believe that this was a targeted, not a random, attack and I am satisfied that there is no wider risk to the public.
"I would appeal to anyone who was in the area and who witnessed the car entering, or leaving, Flynn Gardens shortly before 7.00 pm to get in touch.
"I would urge anyone who has private CCTV to check the footage for anything of significance which may assist our enquiries. If you were driving in the area and your car is equipped with a dashcam I would also ask you to check the footage too."
Additional high-visibility patrols will take place in the surrounding area to re-assure the public.
Chief Inspector Gillian Norrie, the Local Area Commander, said: "The extra patrols by my uniformed officers will continue until further notice. If you have any concerns you can contact police or speak with any of the officers who will be patrolling the area."
Anyone with information can contact Police Scotland on 101 - quoting incident number 3296 of 30 December 2019. Information can also be given anonymously to Crimestoppers on 0800 555 111.