Weber, 33, was expected to need 5-6 months to recover from an arthroscopic procedure to repair a torn meniscus June 19.
"He skated for about 10 minutes as part of his recovery program," coach Claude Julien said. "We're still going day by day. As we speak right now, nothing has changed as part of his timeline."
The Canadiens don't expect Weber to play until December.
"It's always great to see your teammate come on the ice, especially when he's been out as long as he has," Julien said. "Not only are they happy, they're happy for him, mostly that's their reaction. Nice for him to put on his skates after he's been off them for so long. It's a step in the right direction as part of his rehab. Hopefully his rehab goes really well and we've got a player back that's going to be extremely helpful to our team."
The Canadiens were shut out 3-0 by the Los Angeles Kings at Bell Centre on Thursday. Weber, named Montreal captain Oct. 1, skated out with the traditional torch at the conclusion of pregame introductions.
"He's getting closer, which is exciting for our group and exciting for him," forward Brendan Gallagher said. "He's a huge part of our team. Top defenseman in the League, always has been. It's exciting for our team because we know we're going to add a player who can pretty much do it all. He's the captain of our team for a reason. I think we're all looking forward to it."
Weber had 16 points (six goals, 10 assists) in 26 games last season, which ended Dec. 16 because of an injury to his left foot he had surgically repaired March 13.
A three-time Norris Trophy finalist, Weber is second among active NHL defensemen with 189 goals (Zdeno Chara, 196) and fifth with 501 points.