Bojan was expected to start in the Champions League against Milan, but picked up a hamstring problem in last weekend's 6-0 win over the Go Ahead Eagles in the Eredivisie.
After conducting an MRI scan on the injury, Ajax doctors have confirmed that the tear is worse than first thought, ruling the 23-year-old out for at least six weeks.
A club statement read: "Bojan has a tear in his left hamstring. This was revealed by an MRI scan on Tuesday morning. The attacker is expected to be out for four to six weeks."
The Barcelona loanee will now return to Spain for treatment and is not expected to be considered fit for first-team action for Ajax until at least mid-November.