Campbell - controversially captured from fierce North London rivals Spurs on a Bosman free transfer - ended last season struggling with an ankle injury.
He suffered problems with both ankles in the final weeks of last season, and he is still recovering from the injuries.
Campbell sustained ankle ligament damage playing for England in Albania.
He won a battle to be fit for the FA Cup semi-final against Arsenal, but sustained a similar problem in the other ankle and limped off in the first half.
Campbell will definitely miss Arsenal's opening pre-season friendly at Borehamwood.
But Arsenal boss Arsene Wenger remains hopeful the England defender will be available for the opening fixture at Middlesbrough on 18 August.