The Oakland Tribune reported Campbell thinks he could be back in six weeks. Initially it was reported he was out for the year.
Campbell was hurt in the second quarter Sunday when Cleveland linebacker Scott Fujita landed on top of him during a scramble.
He was replaced by Kyle Boller and the Raiders went on to a 24-17 win that left them with a 4-2 record.
Campbell, in the final year of his contract, has amassed 1,170 yards with six touchdowns and four interceptions this season.
Celebrity Families of 2014 [PHOTOS]