Ryan didn't return for the third period Tuesday night during an 8-2 home loss against Chicago, and he wasn't with the Senators for Wednesday night's game in Toronto.
Ottawa coach Guy Boucher couldn't give much of an update on the extent of the injury or how long it will sideline the 30-year-old winger.
"We have to wait until the swelling is down to know," Boucher said when he spoke with media at the Wednesday morning skate.
This is Ryan's third hand injury in 12 months and seventh since 2014. He broke the index finger on his right hand and missed time in November before re-aggravating it in December. It was the same finger he broke in a game last February.
Boucher added that Ryan attempted to play through the pain against the Blackhawks.
"It got worse and worse as the game went on until he couldn't take it," Boucher said.
Ryan has five goals and 12 assists in 32 games this season.
Ottawa begins its bye week Thursday and will have seven days off before returning to the ice Jan. 18 against St. Louis.