The 28-year-old defender sustained a hamstring injury in the FA Cup semi-final win over Manchester City.
An Arsenal statement read: "Right hamstring injury sustained during Emirates FA Cup semi-final on July 18. Further assessments during the week identified a significant injury to the right hamstring.
"As a result, Shkodran had a successful small procedure to his right hamstring on Saturday.
"Shkodran is now in the early stages of his recovery and rehabilitation, receiving specialist attention and support from our medical team.
"Aiming to return to full training in October."