Second-year cornerback Coye Francies also is on the list with an undisclosed injury.
Rogers missed the final five games of the 2009 season with a broken leg and Mosley sat out the final four with an injured ankle.
Rogers still faces a possible NFL suspension, but has avoided trial on a felony gun charge that will be dismissed if the 31-year-old completes 40 hours of volunteer service and 10 hours in a gun class. Police said Rogers had the semiautomatic handgun in a carry-on bag at Cleveland's Hopkins International Airport in April.
Neither Rogers nor Mosley participated in spring drills. Francies, who played briefly in six games as a rookie, practiced in minicamp and had two interceptions.
The trio does not count against the Browns' 80-man training camp roster and cannot practice.
The players aren't the only Browns hobbled as camp begins.
Mike Holmgren is starting his first season as Cleveland Browns president in a leg cast as he recovers from offseason surgery on his right foot.
Information from The Associated Press was used in this report.