Bills general manager Doug Whaley said in a statement that Alonso would be scheduled for surgery "in the near future and begin a rehabilitation program at the appropriate time."
"We feel badly for Kiko because he has worked very hard this offseason in preparation for the upcoming season, but we look forward to his return with his style of play that made him one of the league's outstanding rookies in 2013," Whaley said in a statement.
A seven- to nine-month recovery is expected, a source told ESPN NFL Insider Adam Schefter.
The Oregon Ducks product played every defensive snap last season in his rookie year 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 do have some depth behind Alonso.
The Bills are off until July 18, when players are scheduled to report for the start of training camp in suburban Rochester.
ESPN.com Bills reporter Mike Rodak and The Associated Press contributed to this report.