Clark, who will go under the knife on Wednesday, wrote on Twitter that he will be sidelined for the "foreseeable future". The 23-year-old was included in England's Six Nations squad before suffering the injury to his right AC joint in Northampton's Heineken Cup defeat to Glasgow on Saturday.
Saracens lock Mouritz Botha has joined up with England at their pre-tournament training camp in Leeds as Clark's replacement.
England coach Stuart Lancaster said: "It is a shame for Calum as he had worked hard to get back into the senior squad. But these things happen and our medics will work closely with Northampton on his rehab."
Clark wrote on his Twitter account: "My shoulder needs an operation so I will be out of action for the foreseeable future. That's the game."
Clark was on the fringes of the England squad this time last year, but his career was put on hold by a 32-week ban after pleading guilty to injuring Leicester hooker Rob Hawkins during the LV= Cup final on March 18.
His suspension ran from March 22 to November 1, ruling him out of England's summer tour plans and the QBE autumn international series. However, Lancaster was confident Clark had both the temperament and the ability to thrive at Test level and gave him a second chance.
Speaking after naming his squad, Lancaster said: "He has had a tough lesson to learn and he has learned it.
"I have watched his games closely, the first one being against Leicester. He has been harnessing the competitive nature he has got, which you want in players to win games, but he is channelling that in the right way.
"He has had tough lessons to learn. I have coached him since he was 14, I probably know him better than most. I know what he can offer. In addition to his desire to win, his versatility in the second row is an option for us. He is incredibly athletic and very good in the contact areas."
- Sports & Recreation