The France-born Capuozzo, who plays for French club Toulouse, has been one of the stars of the tournament in spite of Italy losing all three of their games so far.
He was key to Italy ending their 36-match losing streak in the competition in Cardiff against Wales last year.
"Given the persistence, of the painful symptoms in the right shoulder and to allow the player to recover peacefully ... the technical and medical team of Italy has decided not to include Capuozzo in matches against Wales and Scotland," the Federation said.
Capuozzo "will continue his rehabilitation in Toulouse, with the supervision of his club", a press release said.
The federation had announced last week that he had suffered from a "musculoskeletal trauma" in the left shoulder after being injured during the 34-20 defeat against Ireland on February 25.
Italy play their last game at home on Saturday against Wales and will finish in Scotland on March 18.
