After seeing specialists this week, and a hand specialist in Manchester on Wednesday, the England medical team confirmed he has torn the ulnar collateral ligament in the thumb and is expected to be out of action for five weeks.
The Sale Sharks captain will have an operation on Friday in a Manchester hospital.
Robinson said: "This is very disappointing for me as it means I miss England's last two games in the Six Nations at Twickenham and two games for my club, Sale Sharks.
"But I'm looking to be back playing very early in April."
England head coach Andy Robinson commented: "I am hugely disappointed for Jason.
"As England captain he has been an immense figure during the autumn internationals and the Six Nations, leading by example at all times.
"I look forward to having him back in the England squad."
England announce their 30-man squad on Thursday to train for their Six Nations game against Italy at Twickenham on March 12.
Andy Robinson will now have to appoint a third captain this season.