Ovechkin was ejected from the game and on Monday was issued a two-game suspension by the league.
"He will likely avoid surgery, and we anticipate a full recovery," Blackhawks physician Michael Terry said in a statement. "He should be ready to play in approximately seven to eight weeks."
Ovechkin on Tuesday said he was disappointed by the suspension.
In a brief interview with reporters in South Florida, the two-time MVP first said he was sorry that the hit resulted in an injury for Campbell and added that he was "disappointed" it resulted in a two-game suspension.
"I didn't mean to make someone injured," Ovechkin told reporters. "But you know, it's a hockey game."
Ovechkin drove Campbell into the boards from behind in the first period Sunday and received a major penalty and a game misconduct. The Blackhawks defenseman stayed down for several minutes before he was able to leave the ice with a trainer. He did not return to the game.
The injuries mean the 30-year-old Campbell's streak of consecutive regular-season games, which reached 388 on Sunday, is over. Chicago's regular season ends April 11, and Campbell could return by mid-May if the Blackhawks are still in the playoffs.
Campbell is a three-time All-Star who has seven goals and 31 assists this season.
Information from The Associated Press was used in this report.