The forward will be out 4-6 weeks. The regular season ends April 4, four weeks from Saturday.
"That's usually the case," Philadelphia coach Alain Vigneault said Thursday of the time frame. "It's a finger. Wasn't much of a shot. Just little wrister, got him in the right spot."
Van Riemsdyk was struck in the hand by a shot from Capitals defenseman Jonas Siegenthaler with 9:17 remaining in the first period.
Van Riemsdyk had 40 points (19 goals, 21 assists) in 66 games this season.
Joel Farabee was recalled from Lehigh Valley of the American Hockey League and the forward was in the lineup when the Flyers played the Carolina Hurricanes at Wells Fargo Center on Thursday.
Philadelphia had won seven straight games and was one point behind Washington for first place in the Metropolitan Division.
"He's an elite player in this league," Flyers center Kevin Hayes said of van Riemsdyk. "There's a reason why he scores 25-plus (goals) every year and he brings a lot to this team. But we have guys in the minors that have played a lot of games this year that have contributed, and I'm expecting the same thing."
