The ban comes after White took several strides towards Kent Huskins in Monday's loss to the Flyers, hitting the Philadelphia defenceman in the head. White was given a match penalty for attempt to injure, and ejected.
NHL disciplinarian Brendan Shanahan said in the league's explanation video that while Huskins was eligible to be checked on the play, White had time to aim for the veteran defender's body, but instead drove upwards and towards the head.
White, who is a restricted free agent at season's end, was suiting up for the Habs for the first time in nine days.
He has one assist in 25 games this season, with 67 penalty minutes.
The earliest White would be eligible to return is the season finale against Toronto on Hockey Night in Canada on April 27, but he might have difficulty drawing back in if it is a game of importance for the Habs.
Montreal's immediate challenge is a game against Pittsburgh on Wednesday night.