The Scotland international suffered the problem during Tuesday's goalless draw at Bristol City in the Championship.
Manager Gus Poyet has revealed that the club is now looking to bring in a replacement as the Seagulls battle for promotion to the Premier League.
"We have two weeks of the loan window left and we cannot afford to finish the season with just two strikers," he is quoted as saying by Sky Sports News.
"We are still there or thereabouts and there are options, but it's complicated."
Mackail-Smith, who has scored 11 goals in 31 games this season, will undergo surgery next week.