The 29-year-old was substituted midway through the second half of Brighton's home game against Birmingham City - a match in which they were 1-0 victors courtesy of a goal from David Lopez.
Crofts was forced to miss several matches for Brighton last year through injury and manager Oscar Garcia paid tribute to the Wales international for the contribution he has made to the side this season.
"I am very sorry for Crofty, he has been excellent this season and a key player," Garcia told the club's official website. "He wanted to play a big part in our season after missing so much of the last campaign through injury.
"Of course, he has already done that, with his performances and the key goals he has scored, and he will be a big loss - but we have a good squad with strength in depth to deal with this type of situation."
Crofts is expected to be sidelined for at least six months and looks set to return for Brighton during pre-season at the earliest.
He will undergo knee surgery later this week, and Garcia added: "On behalf of all at the club I would like to wish him a speedy recovery."
Brighton moved into the top six in the Sky Bet Championship courtesy of the victory over Birmingham, but Garcia is refusing to get carried away, insisting there is plenty of football to be played between now and the end of the season.
"I prefer to see the performance of the team," Garcia said. "Some games we played well yet didn't win. We have to keep going and at the end of the season we'll see where we are."