Brown was forced off after just six minutes on Monday night as Albion claimed a 2-1 FA Cup win over the Eagles.
Manager Chris Hughton had hoped the injury would not be too serious, but the winger has announced on his official Instagram account that he requires surgery and will not be able to return this season.
“Not the news I wanted to hear, I have torn my ACL & it will need surgery to fix,” he wrote. “I will come back fitter & stronger and hopefully be ready for next season.
“Thank you to everyone at Brighton for the love and support they showed towards me, the fans, the staff, & all the players.
“I’ve met some amazing people here & these memories will be with me forever. See you all next season.”
Brown, 21, is on a season-long loan deal at Brighton from Chelsea and is now expected to return to his parent club for treatment on the injury.