Officers were initially called to the residence in the Hobart suburb of Goodwood about 4.30am on Sunday.
The incident escalated and the 34-year-old allegedly threatened to use a firearm during a confrontation outside the home just before 6am.
Tasmania Police Southern District Commander Jason Elmer said about 10 officers attended the scene where pepper spray was used on the man.
Two officers then fired their weapons wounding him in the chest.
"This was a very dynamic situation...at the time they (officers) discharged their firearms they were firmly of the belief that he was in the possession of a firearm," Mr Elmer told reporters.
The man allegedly refused to put his hands in the air and threatened to shoot officers with a weapon.
But Mr Elmer said the man did not carry a firearm.
"Post-shooting of him it's been ascertained the male was not in possession of a firearm," he said.
The man was alone at the property and is a relative of the owners who called police believing there was a trespasser.
He was given first aid at the scene and transferred to hospital, where he remains in a serious but stable condition.
"This a traumatic event... they (the officers) have had to take action this morning that will no doubt imprint upon them for the rest of their lives," Mr Elmer said.
A professional standards investigation is under way.
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