Steven Anderson was stopped from boarding a flight to the Caribbean island by Delta Air Lines staff at Hartsfield-Jackson Atlanta International Airport in Georgia.
Officials from the country, where homosexual intercourse is illegal, said the 36-year-old's comments were "not conducive to the current climate".
Mr Anderson told the Jamaican Gleaner newspaper that he planned to visit the island for "missionary work" with his 14-year-old son, adding: "I was kind of surprised that Jamaica would ban me for my views on homosexuality."
The leader of Faithful Word Baptist Church in Phoenix, Arizona previously said during a sermon that homosexuality should be punishable with being stoned to death.
It emerged in September 2016 that Mr Anderson had been banned from the UK and South Africa, following a claim that the victims of a shooting at a gay nightclub in Orlando were paedophiles.
At the time, a Home Office spokesman said: "The Home Secretary has the power to exclude an individual if she considers that his or her presence in the UK is not conducive to the public good or if their exclusion is justified on public policy grounds.
"Coming here is a privilege that we refuse to extend to those who seek to subvert our shared values."
An online petition calling for Mr Anderson to be denied entry to Jamaica received more than 38,000 signatures.
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