Police in the tourist resort town of Negril, west of here, said Castillo, from Las Vegas, Nevada, was hit by the jet ski, which did not stop.
The American, who was vacationing with his wife, was rushed to hospital where he was pronounced dead.
In recent months there have been several complaints about jet skis being operated in areas reserved for swimming.
Last October, Tourism Minister Wykeham McNeill told Parliament that there would be a six-month suspension on the importation of all jet skis for commercial use.
He also said that the Ministry of Tourism had held talks with the marine police and the Jamaica Defence Force Coastguard about actions to be taken against illegal jet ski operators