The play delves into the psyche of a boy named Alan Strang who blinds six horses with a metal spike. The production is scheduled to open next March in the West End theater district, said spokesman Peter Thompson.
"It is an extraordinary play, and he's very much looking forward to the role," Radcliffe's spokeswoman, Vanessa Davies, said Friday. "He is maturing as an actor and beginning to take on new and challenging roles."
In one scene the actor playing Strang is required to simulate sexual ecstasy while riding a horse naked. But Davies said nudity was not the focus of the play.
Richard Griffiths, who plays Harry's Uncle Vernon in the films, is lined up to play the psychiatrist who interviews the troubled youth.
Radcliffe is now filming "Harry Potter and the Order of the Phoenix," the fifth installment in Harry's adventures, and recently finished shooting "December Boys," the story of four orphans who compete for adoption.
"Equus" opened in 1973 at London's National Theatre, before a successful run on Broadway starring Anthony Hopkins. Richard Burton starred in a 1977 film adaptation.