Radcliffe is set to star in Equus in New York next year after the resounding success of the show in London's West End.
But in an interview with the Reuters news agency he admitted that he would be wary of the American audiences, most of whom will only know him as the boy wizard of JK Rowling's books.
"It will be amazing, but I will be terrified because I was talking to Richard Griffiths [who also starred in Equus] about playing New York and he said the most stupid thing you can do is underestimate New York audiences," he said.
The 18-year-old delivers a nude scene in Peter Shaffer play and received a standing ovation on the opening night of his theatrical debut at the Gielgud theatre in February.
He appears as troubled teenager Alan Strang, who has an erotic and destructive relationship with horses.
It is expected that the show will cross the Atlantic and play in American theatres early next year.
"I would be very nervous because I think [the audiences are] even more discerning than in London," Radcliffe added.
"But I know we have a good show, it was a good show when we did it in London and hopefully if we do it again it will still be that good. It has to be better."
Radcliffe's latest film December Boys, in which he stars as the leader of a group of young Australian outback orphans, is out in the UK later this month.
