According to his agent at TEAM8 Tony Godsick, the 17-time grand slam champion suffered a torn meniscus last Friday, the day after his Australian Open semi-final exit in four sets to Novak Djokovic.
It is not clear how the Swiss master sustained the injury.
Federer has withdrawn from the World Tennis Tournament in Rotterdam from February 8-21 and the Dubai event from February 22.
“I am so disappointed to have to miss Rotterdam and Dubai as they are two of my favourite tournaments on the ATP World Tour,” said Federer, who is the reigning champion in Dubai having won the title last March for the seventh time.
“While this is an unfortunate setback, I feel grateful that up until now I have remained mostly healthy throughout my career,” the 34-year-old Swiss added.
“My doctors have ensured me that the [arthroscopic] surgery was a success and, with proper rehabilitation, I will be able to return to the tour soon.”
The world No.3 has won two Rotterdam trophies among his 88 career titles.
By skipping Rotterdam and Dubai, Federer hopes to be fit to return to the court in California at the Indian Wells event from March 7.
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