The 24-year-old didn't appear in Saturday's preseason game against the Tampa Bay Buccaneers.
Turron Davenport of ESPN reported Brown also wasn't available during joint-practices with the Buccaneers, with head coach Mike Vrabel providing limited information.
In his third NFL season, Brown is set to be paired with Julio Jones to create one of the sport's most dynamic one-two punches at receiver. Jones came to Tennessee via trade this offseason after a decade with the Atlanta Falcons.
If Brown is slated to miss any significant time, the onus will be on the 32-year-old to produce at his typical WR1 level.