A statement shared by his agent on behalf of the family said Wilkinson died suddenly at home on Saturday. It didn't provide further details.
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Wilkinson was nominated for a best actor Academy Award for his work in 2001's family drama "In The Bedroom" in 2001 and in the best supporting actor category for his role in "Michael Clayton," a 2007 film that starred George Clooney.
He is remembered by many in Britain and beyond for playing former steel mill foreman Gerald Cooper in the 1997 comedy "The Full Monty," about a group of unemployed steel workers who formed an unlikely male stripping act.
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Wilkinson appeared in dozens of other movies, including "Batman Begins," "Eternal Sunshine of the Spotless Mind" and "Valkyrie."
The actor was recognized for his services to drama in 2005 when he was appointed a member of the Order of the British Empire.