Hunter made 726 appearances for Leeds in 15 years at the club and earned the nickname "Bites yer legs" for his tough tackling.
"We can confirm that Leeds United and England legend Norman Hunter is being treated in hospital after testing positive for COVID-19," Leeds said in a statement.
"We would like to take this opportunity to remind the public and the media to respect the wishes of Norman and his family and to give them the space they need during this difficult time."
Hunter, 76, won two league titles, an FA Cup and a League Cup with Leeds and played in their 1975 European Cup final defeat by German side Bayern Munich.
He was also part of England's 1966 World Cup-winning squad and was the first winner of the PFA Players' Player of the Year award in 1974.