"We do not have the details at this point, but early indications are that it could be significant," general manager Doug Whaley said in a statement Tuesday evening.
The Bills said they learned of the injury Tuesday but did not specify when or how it occurred. A seven- to nine-month recovery is expected, a source told ESPN NFL Insider Adam Schefter.
Alonso finished second in The Associated Press' NFL defensive rookie of the year voting last season. The Oregon Ducks product played every defensive snap last season and ranked third in the NFL with 159 tackles.
Under new defensive coordinator Jim Schwartz, Alonso was expected to shift from middle to weakside linebacker in Schwartz's 4-3 scheme. The team wanted to "free up" Alonso to make more plays from the outside of the formation and signed Brandon Spikes this offseason to replace Alonso at middle linebacker.
Alonso already was recovering from hip surgery this offseason. The procedure, to repair a torn labrum, was performed sometime in January, a league source told ESPN's Adam Caplan.
The Bills are off until July 18, when players are scheduled to report for the start of training camp in suburban Rochester.
The Associated Press contributed to this report.