Hunter-Reay is the first American driver to win the Indianapolis 500 since Sam Hornish Jr. in 2006.
Castroneves was trying to make history as just the fourth driver to win four Indianapolis 500 races.
"It's a shame, I want to give this to Roger (team owner Penske) so bad," Castroneves said. "It was a great fight. I tell you what guys. It was a great TV...I was having a great time."