The former England skipper injured his left shoulder during Harlequins' English Premiership defeat at Worcester on New Year's Day
The former England skipper, 30, injured his left shoulder during Harlequins' 24-17 English Premiership defeat at Worcester on New Year's Day and was due to go under the knife on Monday.
It will keep him out of England's entire Six Nations title defence, which begins against France at Twickenham on February 4 and concludes against Ireland in Dublin 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," Quins said in short statement on their website.
"He is expected to be out of competitive action for around 12 weeks. Harlequins will provide relevant updates on his progress as appropriate."
Although he lost the captaincy to Dylan Hartley following Eddie Jones's appointment as head coach, Robshaw -- capped 55 times -- played a key role as England registered a perfect run of 13 wins in 2016.
His absence is the latest blow for Jones, who already had injury doubts over forwards Joe Marler, Mako Vunipola and James Haskell.
Billy Vunipola will miss the early rounds of the Six Nations after undergoing knee surgery and Hartley will be short of match fitness after his six-week suspension.
Flanker Haskell lasted only 35 seconds in his comeback from a toe injury in Wasps' 22-16 win over Leicester on Sunday after suffering a concussion as he tackled Freddie Burns.
Wasps rugby director Dai Young said Haskell was "totally fine", but the 31-year-old must nonetheless undergo the usual concussion protocols before he can return to action.
His Quins team-mate Marler has been nursing a calf injury, while Mako Vunipola is yet to return to action after a knee problem.
Saracens lock George Kruis (fractured cheekbone) and Wasps lock Joe Launchbury (calf) are also currently on the sidelines, although they are expected to return to action soon.
Northampton hooker Hartley will be available for England's Six Nations opener against France, but he will have only just completed his ban for striking Leinster's Sean O'Brien.