When Iranian civil aviation officials identified the plane, they could not find it in their system because it was supposed to have flown through hours earlier, the official said.
Iranian officials first asked it to turn around and then to land at Bandar Abbas, Iran, when told it did not have enough fuel to return to Afghanistan, the official said.
Fly Dubai confirmed in a statement its charter "is now en route to Dubai."
Washington and Tehran have had an antagonistic relationship for decades. The United States cut diplomatic ties with Iran in April 1980, five months after Iranian students occupied the U.S. Embassy in Tehran and took U.S. citizens hostage. Fifty-two Americans were ultimately held for 444 days.
The two countries are now at odds over the Iranian nuclear program, which Washington suspects is aimed at building a bomb but which Iran says is for strictly civilian purposes.
Washington, which has spearheaded sanctions against Tehran for its refusal to give up sensitive uranium enrichment work, is negotiating with other major powers to try to get Iran to curb its nuclear work in exchange for sanctions relief.