Coach Lindy Ruff did not discuss the severity of the injury, but mentioned that the 31-year-old was expected to be out for "some time."
In 43 games with the Sabres this season, Regher has tallied two assists and 32 penalty minutes.
Team owner Terry Pegula recently blamed the club's injuries for its underachieving struggles and stated that he was confident things would bounce back for the second half of the season.
Pegula added that it was difficult to assess the team's needs and that it was too early to consider a shakeup.
The Sabres have had 18 players miss at least one game because of an injury, including starting netminder Ryan Miller, blueliners Tyler Myers and Christian Ehrhoff and forward Ville Leino.
The club hopes to have a full body of healthy players by the NHL's All Star break in two weeks, allowing management to reflect on possible trades to boost the Sabres' playoff hopes.
More Trade Deadline Info
List of Trades
| No-Trade/No-Movement Clauses
| Top 25 Available Players
| Team-by-Team Cap Info