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"At this point, we aren't concerned this injury will jeopardize his season," McDermott said.
There is no timetable for Jones' recovery.
Jones disappointed as a rookie last season after coming out of the draft as the No. 37 overall pick in the second round. The 23-year-old caught 27 passes for 316 yards and two touchdowns in 15 games.
After the season, Jones' father, former Pro Bowl linebacker Robert Jones, appeared on a podcast and revealed his son played through a torn labrum for the majority of the season that required surgery in January.
Zay Jones was arrested on a felony vandalism charge in March following a bizarre incident in Los Angeles in which he allegedly broke a window and glass door at an apartment building. Prosecutors later dropped the charges, citing "insufficient evidence."
Jones is expected to step up this year as part of an unestablished Bills receiving corps that features Kelvin Benjamin as the only other returning receiver to amass at least 200 yards last season. Buffalo selected two receivers in last month's draft: Sixth-round pick Ray-Ray McCloud and seventh-rounder Austin Proehl.
--Field Level Media