"Robben will be out for a long time," manager Jose Mourinho told the club's official Web site (www.chelseafc.com) on Friday.
"He needs surgery and we lose an important player maybe for the rest of the season. For me it is a bit difficult to accept because he played two (Euro 2008 qualifying) matches for his country (in a week) and on Thursday he came here injured."
Netherlands were held to a 0-0 draw by Romania last Saturday before winning 1-0 in Slovenia on Wednesday.
Robben's loss will be softened for Chelsea by the news that England midfielder Joe Cole is poised to return to full training after a long absence.
"Joe Cole is coming back and maybe next week we have him," said Mourinho. "If I can lose one (player) and gain one, it is not so bad.
"At this time we just want to have no more injuries because the matches are arriving and all of them are like finals."
Chelsea are approaching the climax of the season chasing an unlikely quadruple.
The Londoners have already won the League Cup and occupy second place in the Premier League. They are also through to the semi-finals of the FA Cup and the quarter-finals of the Champions League.
Midfielder Frank Lampard, who missed England's 3-0 win over Andorra in a Euro 2008 qualifying tie on Wednesday due to a damaged wrist, has been given the all clear to play in Saturday's league game at Watford.
"Frank's fitness is good," said Chelsea assistant manager Steve Clarke. "He has trained the last couple of days with a cast on and feels much more comfortable with the injury."
