The 52-year-old will undergo surgery later this week and is expected to be absent from coaching duties for some time.
Kevin Sheedy: "It's not ideal but I have to remain positive.
"After a period of rehabilitation I will return to my coaching role at Everton.
"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."
Sheedy started his career with Hereford United, followed by a short spell with Liverpool, but played just three competitive games in four years and was sold to Everton for £100,000 in 1982.
At Everton he made 357 appearances (12 as substitute) and scored 97 goals.
Sheedy's most notable achievements were as part of the 1984 Everton team that won the FA Cup (although he missed the final through injury).
In 1985 and 1987 he won the Football League, and in 1985 the European Cup Winners' Cup, scoring in the final itself.
In the 1980s Sheedy scored the most goals from free-kicks in the top-flight of the English football league.
He was selected in the PFA Team of the Year in both Everton championship winning years of 1985 and 1987.
Sheedy left Goodison Park in 1992 on a free transfer to join Newcastle United, and helped them win the Division One title, and promotion to the Premier League, in 1992–93.
He ended his career with Blackpool in the 1993–94 Division Two campaign.