Steven Anderson and members of the Faithful Word Baptist Church of Tempe, Arizona, will not be allowed to travel to South Africa because they allegedly promote hate speech and "social violence", said Malusi Gigaba, the home affairs minister.
Anderson had been due to attend a church event in Johannesburg on Sunday but his visit had always been in doubt amid protests at his views on LGBT people.
Homosexuality is "an abomination punishable by the death penalty," according to Anderson's church.
South Africa is still struggling to curb discrimination despite laws that are among the most "progressive" in the world, and the country does not "need more hatred advocated to our people," Mr Gigaba said.
"I have identified Steven Anderson as an undesirable person to travel to South Africa," he added.
Anderson promised to go ahead with a planned trip to Botswana for a September 25 event, though.
"I feel sorry for people who live in South Africa, but thank God we still have a wide open door in Botswana," Mr Anderson said on Facebook. "Stand by for reports of MULTITUDES saved in Botswana, where religious freedom still exists."
