The 24-year-old rookie suffered a gash to his right femoral artery and vein during a practice Thursday.
His family released a statement Monday thanking the Jets training staff and players for their quick action.
The Redmonds say they saved his life.
Redmond was accidentally cut by a teammate's skate during a drill.
He was taken to hospital where he underwent a three-hour surgery to repair the injury.
"We are eternally grateful for the quick response of the Winnipeg Jets training and coaching staff as well as Zach’s teammates, who without reservation jumped to his aid, heroically took control of the situation and made sure Zach was given the proper care, in turn saving his life," the family said in the statement. "Zach is currently in positive spirits, and getting the rest he needs while surrounded by family and friends in a Raleigh area hospital."
Redmond is out indefinitely. He has a goal and three assists in eight games this year.