There remains no timeline for his return to game action.
Price last played on July 7 in Game 5 of the Stanley Cup Final. The Tampa Bay Lightning won the match 1-0 to take the series and the championship for the second consecutive season.
The 34-year-old has yet to play a game this season due to the knee surgery and time spent in the NHL/NHLPA's joint player assistance program.
He started skating in late 2021 but then had to take a step back in his recovery, returning to only off-ice work. Now, he is back on the ice and one step closer to resuming his career.
The Canadiens beat the Edmonton Oilers 5-2 Saturday for their seventh win in the last eight games. Montreal has 26 games remaining this season.
In other injury news, the Canadiens announced that centre Jake Evans is day-to-day with an upper-body injury while Christian Dvorak, Paul Byron, Jonathan Drouin and Jake Allen will join the team in Vancouver and begin practicing in non-contact jerseys.