A government statement did not say why Steven Anderson had been declared a “prohibited immigrant”.
He was arrested after doing a radio interview.
Mr. Anderson runs the Faithful Word Baptist Church, which says that homosexuality is an abomination punishable by the death penalty.
After his Visa for South Africa was rejected last week, the preacher posted on his Facebook page: “thank god we still have a wide open door in Botswana.”
Homosexual acts are illegal in Botswana, as in many African countries.