The injury occurred during a fight in the second period of Saturday's win over the Edmonton Oilers. Video of the fight is embedded below.
Neil is in his 13th season in the league. Over 38 games this season, the 35-year-old has recorded four goals and three assists.
The Senators (22-22-10) currently sit in sixth place in the Atlantic Division of the Eastern Conference.
Ottawa will host the Carolina Hurricanes on Monday.
[via YouTube user hockeyfights.com]