"He had a very deep laceration," Wings GM Ken Holland said. "No damage to any tendons, but some of the muscle was detached. During surgery, Dr. (Doug) Plagens reattached some of the muscle.
"All went well."
White, 28, left during the third period of Tuesday night's 2-1 loss to the Dallas after he was cut by Jimmy Howard's skate and was sent to hospital for treatment.
Fellow blueliner Carlo Colaiacovo will be out for three to four weeks with a shoulder injury, while defensemen Jonathan Ericsson and Jakub Kindl are still dealing with injuries.
"Injuries are a part of the game," Holland added. "Some years you get good luck with them. Early on we've been hit with a rash.
"When we get bodies back, it takes a while to get them going. We have to find a way to grind out wins."
In 77 games with the Wings last season, White collected seven goals and 25 assists for 32 points.