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.
Three Cleveland Browns starters skip mandatory minicampHleb set for Barca return
