The fracture failed to heal satisfactorily and Gibbs will now have a bone graft to help ensure a full recovery.
The 20-year-old's rehabilitation is expected to take around five months.
"Needless to say I'm gutted - there's just no other word," the England Under-21 international told The Official Arsenal Magazine.
"The other option to surgery would have been to wait and let the bone grow in my foot, but we didn't want to do that because I'd have to wait another six weeks just to have another scan.
"I'd run the risk of it carrying on into next season, and we don't want to do that."
Gibbs added: "I'm now just looking to recover from the injury, work really hard and be ready for next season."
The left-back had been suggested as a potential member of Fabio Capello's World Cup squad this summer before his injury.
Arsenal have cover in the position with French youngster Armand Traore backing up first-choice Gael Clichy.
Barclays Prem Top Goalscorer 09/10: Fabregas, C. 33/1