Johnsson suffered the injury Thursday against the Dallas Stars after colliding with teammate Kasperi Kapanen.
Johnsson likely won't return for the rest of the regular season. An exact eight-week timeline would have him back in the lineup April 10, but Toronto's last regular-season game is April 4. However, he could be back for the playoffs, should the Leafs qualify.
The 25-year-old has recorded eight goals and 21 points in 43 games this season. He missed 15 contests earlier in the campaign with a leg injury.
Johnsson's name has been involved in trade rumors as the Leafs' search for a defensive upgrade continues, but his latest injury could affect his trade value.
The former seventh-round pick signed a four-year contract carrying a $3.4-million cap hit following a 20-goal rookie season in 2018-19.