Robben returned with a swollen knee after playing in the Netherlands' 0-0 draw with Romania and 1-0 win over Slovenia in Euro 2008 qualifiers over the last week.
"A scan was organised immediately which confirmed a complex tear of the lateral meniscus within the knee," club doctor Bryan English was quoted as saying on Chelsea's Web site (www.chelseafc.con) on Saturday.
"Arjen underwent arthroscopic surgery in London... It will be at least four weeks before he returns to full fitness," English said.
Manager Jose Mourinho, whose side have a packed schedule until the end of the season in May, vented his frustration on Friday.
"For me it is a bit difficult to accept because he played two matches for his country and on Thursday he came here injured," Mourinho was quoted as saying on the Web site.
Robben is an important creative force in Chelsea's attack but has suffered frequent injuries since he arrived at Stamford Bridge in 2004.
"At this time we just want to have no more injuries because the matches are arriving and all of them are like finals," Mourinho said.
The London side, who have already won the League Cup, are second in the Premier League and are through to the semi-finals of the FA Cup. They meet Valencia in the first leg quarter-finals of the Champions League on Wednesday.
Attacking midfielder Joe Cole, who has been out for most of the season through injury, could be back next week and his England team mate Frank Lampard has been cleared to play despite missing his country's win over Andorra on Wednesday with a damaged wrist.
Chelsea meet bottom side Watford away in the Premier League later on Saturday.
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