Nicholas Aaron Scott 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 Scott, 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, later identified as Scott, and another man inside with head injuries.
"We located Nicholas at the scene a number of hours later at Granton. We have spoken with his next of kin," Detective Inspector Troy Morrisby said.
The injured man was taken to Royal Hobart Hospital with non-life-threatening injuries.
Morrisby said the man has been treated and is in a stable condition.
"We do have a male in custody at the moment assisting with inquiries. That man will be interviewed," Morrisby said.
He said the man who is in custody is also known to police.
"We have had prior dealing with that male," he said.
Morrisby said the two men were known to each other and there is no wider risk to the community.
"It wasn't a random attack or random shooting," he said.
"We certainly don't believe at this point in time there is greater ongoing risk to the broader community."
Morrisby said the Black Snake Road address is known to police due to a "small cohort of people who have resided there".
"The overwhelming majority of the street is occupied by law-abiding residents. But yes we're aware of the address," he said.
"We have attended before."
He added the home normally has two other people, a young man and a woman, residing there at the time.
"Thankfully, neither of those were injured in relation to that address but they are regular occupants," Morrisby said.
Police are investigating how the man escaped custody and how the shooting unfolded.
