The Honduras midfielder reported the complaint to the Tottenham medical staff the day after the club's 0-0 draw with AC Milan and underwent an arthroscopy - a minor operation - on Saturday.
The 26-year-old has played 30 times for the club this season, his most recent appearance being Tottenham's 3-1 defeat at Blackpool two and a half weeks ago.
He was a regular in the Spurs XI last season but has found himself used more sparingly this term, with manager Harry Redknapp preferring to use Tom Huddlestone, Luka Modric, Jermaine Jenas and Brazil midfielder Sandro in central midfield.
Palacios will miss Tottenham's Barclays Premier League matches against West Ham and his former club Wigan, but should have recovered in time to be available for the first leg of the club's Champions League quarter final - the draw for which is made next Friday.
Source: PA
Source: PA