Shaw had two assists, one shot on net, one hit, and a two-minute minor penalty in Saturday's 6-4 loss to the Capitals.
Shaw registered an assist through 13:56 of ice time during Friday's 3-0 win over Buffalo.
Shaw -- who was held out Saturday as a potential trade chip -- is expected to return to the lineup against the Flyers on Monday, John Lu of TSN.ca reports.
Shaw will be held out of Saturday's matchup against the Lightning as the Canadiens take part in trade talks.
Shaw scored a goal on four shots and had three hits in Thursday's 5-3 loss to the Flyers.
Shaw was in Montreal's active lineup Friday for the first time since being claimed off waivers. He had one hit and one blocked shot in 10:36 of ice time in a 3-2 win over Washington.
Shaw was picked up off the waiver wire by the Canadiens on Monday.
Shaw was placed on waivers by the Ducks on Sunday, Elliotte Friedman of NHL Network reports.
Shaw scored a goal and added an assist Monday in a 3-2 win over Carolina.
Shaw missed the scoresheet for the 13th consecutive game during Wednesday's 3-0 win over Ottawa.