Matthews limped off the field Monday after hurting his knee while running a route during warmups. Medical testing confirmed the diagnosis Wednesday.
Matthews, a nine-year veteran who has 274 catches as a receiver, switched to tight end last year. He spent most of 2021 on the team’s practice squad.
The 49ers have Ross Dwelley, Tyler Kroft, Tanner Hudson and Troy Fumagalli behind George Kittle. Charlie Woerner, the No. 2 tight end as a rookie, is on the active/physically unable to perform list while rehabilitating from core muscle surgery.
San Francisco lost defensive tackle Maurice Hurst to a season-ending torn biceps last week.