The club confirmed Wednesday morning that the Croatia international underwent surgery on Tuesday night, meaning he could now miss the Champions League last-16 first leg at AC Milan on February 15.
He will also sit out Wednesday night's Barclays Premier League game at Blackburn and will be unavailable for Saturday's home clash with Bolton and the following weekend's trip to Sunderland.
Tottenham said in a statement: "Luka Modric has undergone surgery to remove his appendix.
"The Croatia midfielder was diagnosed with acute appendicitis after contacting our medical staff complaining of abdominal discomfort.
"He is likely to be sidelined for around two weeks."
The 25-year-old has been in sparkling form for Spurs for the past few months and his loss is a huge blow for manager Harry Redknapp, who is already without key midfielders Gareth Bale (back) and Tom Huddlestone (ankle).
Redknapp has even bigger problems in defence, with Younes Kaboul on Tuesday undergoing surgery on a knee injury and captain Ledley King also set to go under the knife.
Michael Dawson is suspended and William Gallas is struggling with a hip injury for Wednesday night's game at Ewood Park, meaning Jonathan Woodgate could make his first appearance for 14 months.
Source: PA
Source: PA