The 26-year-old suffered the blow during Brighton's 1-1 draw with Blackburn Rovers in the Championship fixture on Tuesday.
"Hosko has been working so hard and got his opportunity against Blackburn," Brighton midfielder Dean Hammond told BBC Sussex.
"He is a great player and deserved his chance. He has not had the luck so all the lads and I feel very sorry for him. We will be there for him if he needs our support."
Hoskins has featured 12 times for the club this season.