Wild General Manager Chuck Fletcher said Backstrom underwent successful core muscle surgery on Tuesday by Dr. William Meyers in Philadelphia.
Zucker also had surgery on Tuesday to repair a tendon in his left quadriceps with Dr. Michael Stuart at the Mayo Clinic.
Fletcher indicated both players are expected to be fully recovered for the start of the 2014-2015 season.
The Associated Press reports Backstrom had been bothered most of the season with the injury. He has not played since Jan. 30. He was 5-11-2 record for the Wild with a 3.02 goals-against average and an .899 save percentage.
Zucker underwent a minor procedure in February and was hoping to return, but last week he was ruled out for the remainder of the season.
Zucker had four goals and one assist in 21 games with the Wild this season.