Swinney said that if Rodgers' rehab after surgery goes well, he could return for the 2019 season.
"Amari injured his right knee in practice on Monday and will have surgery next week," Swinney said in a statement Wednesday. "He's got a great attitude and he's a grinder. I have no doubt he'll come back better than ever."
Rodgers acknowledged the injury in a Twitter post Monday night, commenting that he "would be back better than ever."
Rodgers was Clemson's third-leading receiver last season, catching 55 passes for 575 yards and four touchdowns, while also serving as the Tigers' primary punt returner, registering 299 return yards and one touchdown.
If Rodgers misses the 2019 season, Clemson remains in solid shape at receiver.
Rodgers is the son of former Tennessee star and current Vols assistant Tee Martin.
The Associated Press contributed to this report.