The Maple Leafs placed the 21-year-old on injured reserve, but he told reporters that he will not need surgery.
Matthews missed 20 games last season, including 10 after separating his right shoulder. He said that this injury is similar but to the opposite shoulder.
"It's part of the game," he said. "I'm going to work as hard as I can to get back as soon as possible."
Matthews was injured in the second period of Saturday's 3-2 win over the Winnipeg Jets. The center was cutting in front of the net with the puck, but as he attempted to shoot, he found himself on the receiving end of a shoulder-to-shoulder hit from Winnipeg defenseman Jacob Trouba.
"I knew the guy was coming," Matthews said. "(I was) trying to get a shot off, but you don't really know what to expect because you're so close to the goalie. He took body, which is what you're supposed to do, and just caught me on a weird angle."
"You want to be out there so bad," Matthews said. "Watching the game is probably the worst part. (Not) being around your teammates, being a part of something, I think that's kind of the hardest thing."
Coach Mike Babcock, whose team is 8-3-0 entering Monday night's game against Calgary, said he talked with Matthews about how best to deal with the setback.
"Be around the group, do what you do, train real hard," the coach said. "Be better when you come back than you were."
Averaging 3.73 goals per game this season -- the third-best mark in the league -- the Maple Leafs are one of the NHL's deepest teams at forward. The Leafs came back from a 2-0 deficit to the Jets on Saturday, scoring three consecutive goals in the final 17 minutes of regulation while Matthews was sidelined.
Despite missing 20 games last season, Matthews finished second on the team in goals (34) and points (63).
"He did a ton of work this summer on his shoulders to make sure he was a stronger," Babcock said. "These things happen. It's too bad for the kid and yet it's an opportunity for someone on our team to play more. It's an opportunity for us to dig in and continue to get better."
Information from The Associated Press was used in this report.