The defender has undergone an operation to repair a minor problem that he picked up during pre-season training.
During a press conference in Hong Kong, Shakespeare confirmed that the 32-year-old could be on the sidelines for up to eight weeks.
"Robert reported back for pre-season and got into some discomfort with his ankle," the manager told reporters. "He's had an operation and thankfully it was successful.
"It's unfortunate for Robert but we thought it might be worse. We're expecting him to be out for around six to eight weeks."
Leicester will have a tough start to the campaign as they take on Arsenal at the Emirates on August 11.