The defenseman was injured in the second period of a 3-0 loss to the Los Angeles Kings on Monday.
"It's disappointing for sure, and really disappointing for him I'm sure," Blues coach Craig Berube said Tuesday. "An injury like that's tough. It's tough to see a teammate, a player go down like that with that injury. I feel bad for him. We're losing a great teammate, he's a great guy and a real good hockey player for us."
Gunnarsson, who had two assists in 12 games this season, his seventh with the Blues. He scored three points in 19 Stanley Cup Playoff games to help them win the Cup in 2019.
"That's a guy that has laid it on the line for this organization for a long time," forward Brayden Schenn said after the game Monday. "He's a [heck] of a teammate and a good guy. The guy is an absolute warrior. It's tough to see."
The 34-year-old is in the final season of a two-year, $3.5 million contract ($1.75 million average annual value) and can become an unrestricted free agent at the end of this season.
Blues forward Ivan Barbashev had left ankle surgery Tuesday and will be reevaluated in six weeks.
Barbashev was injured in a 3-2 overtime win against the San Jose Sharks on Feb. 18. He has scored six points (two goals, four assists) in 17 games this season.
St. Louis is also without forwards Robert Thomas (thumb), Tyler Bozak (upper body), Jaden Schwartz (lower body) and Vladimir Tarasenko (shoulder), and defenseman Colton Parayko (undisclosed).
The Blues host the Kings on Wednesday (9:30 p.m. ET; NBCSN).
NHL.com independent correspondent Louie Korac contributed to this report
