Rogers was hurt on Pittsburgh's final drive of Sunday's 45-42 loss to the Jacksonville Jaguars, the Pittsburgh Post-Gazette reported.
The 25-year-old Rogers, who had a season-high five receptions against the Jaguars, is scheduled to become a restricted free agent in the offseason.
An undrafted free agent out of Louisville in 2015, Rogers had a strong season for Pittsburgh in 2016, registering 48 catches and three touchdowns in 13 games.
Rogers finished with 18 receptions for only 149 yards and one score. He was limited to one catch or less in seven of his last nine regular-season games.