A man who had been jailed and was being treated under prison officer guard at Royal Hobart Hospital escaped around 11.50pm on Monday.
This sparked a significant police search for the man, Tasmania Police said.
At around 1.30am, a gun was allegedly fired at a property on Black Snake Road in Granton.
When police arrived, they found a man’s body outside the home and another man inside with head injuries.
The deceased has been identified as the man who escaped custody earlier in the night.
The injured man was taken to Royal Hobart Hospital with non-life-threatening injuries.
He will be interviewed by police later today.
Detective Inspector Troy Morrisby said the shooting is concerning to the community but an investigation is underway.
“I reassure the community that this incident was between people known to each other, and there is no threat to the wider community,” he said.
Police are investigating how the man escaped custody and how the shooting unfolded.