Holmgren said goalie Ilya Bryzgalov was doing better and should be able to play Tuesday in Washington. He was removed late in Saturday's victory because of a lower-body injury.
Rookie defenseman Erik Gustafsson, recovering from wrist surgery, will start skating this week and may be ready to play in 10 to 14 days, according to Holmgren.
Giroux, who will turn 24 next month, was injured late in the second period Saturday, getting inadvertently kneed in the back of the head by teammate Wayne Simmonds.
If Giroux is sidelined for a while, it will weaken the Flyers in several areas: even strength, the power play and the penalty kill.
"He's our best player. He's a big catalyst for us," winger Scott Hartnell said after Saturday's win. "He's so strong with pucks. He's great defensively. We know what he can do offensively as well. Obviously, if he is out, we're going to miss him big time."
Despite a multitude of injuries, the Flyers are atop the Eastern Conference. Among the players on the current injury list are Giroux, captain Chris Pronger (possible concussion), center Brayden Schenn (mild concussion) and Gustafsson.
"When they come back and everyone is healthy, it's going to be scary," Hartnell said. "But the young guys that we have here . . . it's pretty incredible the minutes that they are playing, and they are playing really well."
Those rookies are Matt Read, Sean Couturier, Marc-Andre Bourdon, Zac Rinaldo, Harry Zolnierczyk and Kevin Marshall. Schenn and Gustafsson are also rookies.
Entering Sunday, Giroux was among the NHL leaders in several categories, including points (39, first); assists (23, tied for second); game-winning goals (five, tied for first); and goals (16, tied for fifth). He is also one of the Flyers' best penalty killers, leads the team in face-off percentage (51.5 percent) and is tops among their forwards in average time on ice, at 21 minutes, 28 seconds per game.