Charlton, 76, suffered the fracture after falling down the stairs at his home earlier this week, the Daily Mirror quoted his son as saying.
"The stairs in his house are a bit tricky and awkward and he basically fell down them on Monday night," he told the paper.
Charlton was a member of England's 1966 World Cup-winning team, playing alongside brother Sir Bobby Charlton.
He later enjoyed a successful career in international management, feted in Ireland for leading the country to the World Cups in 1990 and 1994.