The England defender, who missed large parts of last season with ankle problems, feared the worst when he was injured during the 2-1 win over the United States in Chicago on Saturday.
But Campbell said: "I've had an MRI scan and there is no ligament damage, nothing like that. It is really just a bad twist. There will be no operation, and it's not the same ankle I've had the problems with before. I'm relieved.
"Now it's just a matter of getting the fluid away and it will be no more than two or three weeks before it's fine. I'll be back and flying for pre-season training."
Campbell's injuries cost him his place in the Arsenal and England starting lineups last season to young Switzerland defender Philippe Senderos and John Terry respectively.
