The Scottish Premier League Player of the Year sustained the injury whilst on international duty recently and it was feared that he may miss most of pre-season.
With Celtic's pre-season tour of Australia coming up, Hoops boss Neil Lennon wants him to remain at home and get the problem fixed before returning to Glasgow at the end of the month.
"The club asked me to come back but I asked them permission to stay here," Izaguirre said.
"I hope to be here for at least two more weeks to get in good condition before I go back to Scotland.
"In the morning, I always go to the gym every day and get physiotherapy in the evening.
"I'm still sad I missed out on the Gold Cup because my family would have been there to watch me."