The center left a 6-2 win against the Arizona Coyotes on Saturday midway through the third period.
"If at some point we get him back, great," Senators coach D.J. Smith said after practice Wednesday. "When you hear 'long term,' you're thinking three months, four months, five months, six months."
Norris has two points (one goal, one assist) in five games and is third in average ice time among Senators forwards (18:21) behind
Tim Stutzle
(18:32) and Alex DeBrincat (18:29).
Norris missed 15 games last season with a shoulder injury.
"Different injury than the last one, same shoulder, different injury," Smith said. "Is he going to require surgery or not? We're in the middle of that right now. We'll know a little more in the next four-five days but it's long term."
Norris signed an eight-year, $63.6 million contract ($7.95 million average annual value) with Ottawa on July 15 after he set NHL career highs in goals (35), assists (20) and points (55) in 66 games last season. He also led the Senators in face-off percentage (51.1; minimum 150 face-offs).
"He's one of our best players, he's our most responsible centerman at this point in his career with players that he's played against," Smith said. "... He can score, he can do a lot of things. If you take that player out of a lot of teams' lineups, it changes the dynamic."
Smith said the rest of the Senators center group would have to elevate their games in Norris' absence.
"It's unfortunate Josh isn't here to be a part of it, but you've got [Shane Pinto]," Smith said. "... (General manager) Pierre (Dorion) did a great job in having (Derick) Brassard here. You've got (Dylan) Gambrell, you've got (Mark) Kastelic, so there's some guys in the middle there that can help."
The Senators are 4-2-0 and have won four straight following two losses to start the season. They conclude a five-game homestand against the Minnesota Wild on Thursday (7 p.m. ET; TSN5, RDSI, BSN, BSWI, ESPN+, SN NOW).
