If surgery is required, the team's starting left fielder and leadoff batter will be out six to eight weeks.
Replacing Coghlan on the roster is highly touted prospect Logan Morrison, who will have his contract selected from Triple-A New Orleans.
"When Wes hit the walk-off, I went to pie him in the face," Coghlan said. "When I jumped, I landed wrong on my knee. That's how I got injured."
Emilio Bonifacio played in place of Coghlan on Monday night. Manager Edwin Rodriguez said Morrison and Bonifacio will split time in left field, depending largely on which pitchers they are facing.
Rodriguez added that Hanley Ramirez, who hasn't had an extra-base hit in 19 games, may move from No. 3 in the lineup to the leadoff spot. Bonifacio is another option to lead off.
Coghlan had an MRI on Monday, which revealed the meniscus tear.
Rodriguez said the team addressed excessive celebrating and there will not be any more shaving-cream pie rituals.
Coghlan, who has never been on the disabled list, is the latest player to be injured during a celebration. Kendry Morales of the Angels broke his leg while leaping onto home plate after a walk-off home run.
"Right now we're going to see what's going to happen the next couple of days," Coghlan said. "Surgery is a possibility."
The Marlins are 8-3 since the All-Star break, and the team experienced four walk-off wins during its 10-game homestand.
After each one, players celebrated by shoving shaving cream in the hero-of-the-night's face. Donnie Murphy had two of the walk-off hits.
To have easier access to shaving cream, a can was placed on a shelf inside the batting cage just behind the Marlins dugout.
"It's very humbling when the game is taken away," Coghlan said. "It's also unfortunate, especially with the circumstance that happened. If you get injured, you want to when you're out there competing and not when you're celebrating. I think this experience shows that you get injured celebrating."
Coghlan said he hopes his injury serves as a lesson.
"As players we need to be a little more aware," Coghlan said. "It's a game of emotions, and the emotions get the best of you."
Coghlan is batting .268 with five homers, 28 RBIs and 10 stolen bases.