The ban was handed down after an in-person disciplinary hearing Friday with NHL officials.
Thornton hasn't played since last Saturday when he was assessed a match penalty during Boston's 3-2 win over the Pittsburgh Penguins at TD Garden.
Thornton went after Orpik during a stoppage in play, slew-footing him to the ice and punching him twice in the head.
Orpik suffered a concussion and was taken off the ice on a stretcher and transported to the hospital.
"I can't say I'm sorry enough," a repentant Thornton said after the game.
Orpik is still experiencing concussion-like symptoms and took part in a light skating session for the first time Friday.
Orpik had knocked Boston's Loui Eriksson out of the game earlier with a hit that went unpenalized. The Penguins blue-liner subsequently declined to fight Thornton.
Thornton, a first-time offender, has already missed games against Toronto, Calgary and Edmonton.
The 36-year-old from Oshawa, Ont., has three goals and 41 penalty minutes in 27 games this season.