Grand Slam winners England will play their first game against France at Twickenham on Feb. 4 with the tournament ending on March 18.
"Chris Robshaw will undergo surgery on his left shoulder today to repair an injury sustained in the match against Worcester Warriors on New Year's day," Harlequins said in a statement.
"He is expected to be out of competitive action for around 12 weeks."
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The 30-year-old, who has 55 caps, was replaced as captain after Eddie Jones arrived as head coach but featured in all but one match of England's unbeaten 13-test run in 2016.
His name is now added to a lengthening injury list, with Billy and Mako Vunipola sidelined with knee injuries and Joe Launchbury suffering a calf problem.
Centre Manu Tuilagi is out for the season with cruciate ligament damage.
Flanker James Haskell's comeback from six months out lasted just 35 seconds at the weekend before he had to leave the field with concussion.
Lock George Kruis is also doubtful with a fractured cheekbone and captain Dylan Hartley faces a fitness test following a six-week suspension that ends on Jan. 23.
Robshaw was described by Jones in 2015, before he took over, as "not outstandingly good in any area" but has since become the Australian's first choice blindside after playing openside for four years under former coach Stuart Lancaster.
(Reporting by Alan Baldwin, editing by Ken Ferris)
