The Norway international, 29, was substituted in the 36th minute of Tuesday's 2-1 home defeat by Chelsea after a collision with Eden Hazard.
"It's not good news but we have got strength in depth in midfield," Neil said before Saturday's trip to Swansea.
The Canaries are 18th in the Premier League after an eight-game winless run.
Norwich midfielder Alex Tettey needs ankle surgery and is likely to miss the rest of the season, says Canaries manager Alex Neil.