The incident happened on Bryants Hill at about 11pm on Wednesday.
Police were called to reports of four people breaking in and assaulting a man inside.
They believe a firearm was used and say the victim remains in hospital undergoing treatment although he is not in a life-threatening condition.
The burglary is being linked to an incident three miles away at Days Road in Barton Hill, where approximately 20 minutes earlier a woman had her car stolen. This vehicle has been recovered and is being forensically examined. The woman was not injured.
At this stage no one has been arrested in connection with these incidents.
DI Duncan Wood said: “Firstly, I would like to thank the local community for their understanding and assistance while our investigation continues.
“Our investigation, which was launched on Wednesday, continues and people are likely to see an increased police presence in the St George area.
“I would like to appeal to anyone who either saw the car being stolen or saw anything suspicious in Bryants Hill on Wednesday evening.
“Any information, no matter how insignificant you think it might be, could be crucial to helping us locate the offenders.”
Anyone with information is asked to contact 101 and quote crime reference number 5216171825.