The 44-year-old was taken into custody without incident during a police check at a property in the Launceston suburb of Waverley at 11.45pm on Wednesday.

He had been wanted for questioning over a double stabbing at a home in the nearby suburb of Ravenswood in the early hours of November 25.

A man aged in his 30s died at the house, while a woman also in her 30s was rushed to hospital in a critical condition.

Tasmania Police Detective Inspector Mel Groves said the man, who has yet to be charged or formally interviewed, was co-operating with investigators.

Two teenage children of the woman were at the home at the time but were not injured.

Insp Groves said the woman is recovering well and would be released from hospital on Thursday.

"She can be reunited with her family and they can begin this healing process together," she said.

Insp Groves was unable to comment on whether the woman was in a relationship with the man in custody.

Tasmania Police on Wednesday offered a $50,000 reward for information leading to the arrest of the man.

"I'd like to thank the members of the public for their support, for passing on information to us," Insp Groves said.

Police earlier said they "strongly believed" a person or people were harbouring the man.

Investigators have said the man knew his alleged victims.

Australian Associated Press