Domineque Ray, 42, was put to death in the southern state of Alabama for the 1995 rape and murder of Tiffany Harville, 15.
"Due to the nature of his crime, the decision of a jury to condemn him to death and because our legal system has worked as designed, Mr Ray's sentence was carried out," Alabama Governor Kay Ivey said in a statement.
The execution occurred on Thursday after the country's highest court denied a request for a stay of execution.
Alabama carries out the death penalty by lethal injection.
The Supreme Court's ruling lifted a last-minute stay which Ray had won on Wednesday from a federal appeals court.
US court blocks execution of Muslim inmate who requested imam
Judges on that lower-level court had argued that Alabama regularly placed a Christian cleric in the death chamber of Christian inmates "but has refused to provide the same benefit to a devout Muslim and all other non-Christians."
Officials in the conservative state appealed that ruling to the Supreme Court, which has a conservative majority under President Donald Trump.
The First Amendment to the US Constitution forbids public authorities from favouring one religion over another, or from preventing the free practice of faith.
Ray converted to Islam while in prison and demanded the right to be escorted to the death chamber by an imam.
Local news site al.com reported that Ray's last words were in Arabic, and his Muslim spiritual advisor was sitting with his lawyers and journalists in a viewing room.
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