Backstrom, scheduled to become an unrestricted free agent next week, had a 2.48 goals-against average and .909 save percentage with two shutouts in 42 appearances.
The Finnish netminder was poised to see his first playoff action in five years but got injured in the warmup before Game 1 against Chicago. Backstom never played in the five-game series loss to the Blackhawks.
He underwent sports hernia surgery after the Wild were eliminated.
Financial details were not released by the club. the 35-year-old Backstrom just completed a deal that paid $6 million US per season.
For his career, Backstrom has posted 28 shutouts in 369 regular season games, with a 2.43 average and .917 save percentage.
There were reports indicating the Wild had interest in goalie Jonathan Bernier, traded from Los Angeles to Toronto on Sunday.