Sheedy, who racked up 369 appearances for the Toffees during his playing career, is scheduled to have an operation at some point this week.
"It's not ideal but I have to remain positive," Sheedy told the club's official website. "There is a history in the family.
"It's so important that people don't ignore the early signs and symptoms and don't be afraid to consult a GP. After a period of rehabilitation I will return to my coaching role at Everton."
The former Ireland international scored 97 goals for the Toffees during the 1980s.