The ex-England defender feels the 28-year-old is not setting the right example.
Rooney was named skipper of both his club and country this season but was criticised for his recent sending off against West Ham, when he kicked out against midfielder Stewart Downing.
And Campbell has joined the list of Rooney's critics, even though he admitted that the United striker is the only 'sensible' choice for captain.
Speaking at the Cheltenham Literary Festival, the former Gunners defender followed his approval of the 28-year-old's captaincy by commenting:
"But Rooney is doing a fantastic job of losing it [the captaincy]," he said, referring to his recent red card against West Ham.
Campbell had also commented earlier that the Three Lions should 'get rid' of Gary Neville and replace him with Campbell himself in the coaching setup.
England face San Marino at Wembley Stadium tonight in their second Euro 2016 qualifier. They won their first 2-0 in Switzerland.