The six second sequence showed the luminous nighttime trail of what appeared to be a missile before an explosion at very low altitude.
In June, Iran shot down an advanced USA spy drone, which the Islamic Revolution Guards Corps (IRGC) said was flying over southern parts of the country.
Both countries have repeatedly challenged one another's claims, with the USA denying its device violated Iranian airspace, and Tehran denying its drone was hit at all in July.
Provincial governor Gholamreza Shariati told IRNA that the drone belonged to a "foreign" country and that parts of the drone had been recovered in a nearby lagoon.
The drone was taken down on Friday by an Iran-developed Mersad surface-to-air missile, the Iranian Mehr news agency reported.
A US Defense official told the MailOnline: 'There are no reports of a USA drone being shot down'.
The semi-official Mehr news agency aired footage it said showed the missile attack that downed "the aggressor drone".
The alleged incident comes amid seemingly perpetual high tensions between the USA and Iran, whose rivalry has increasingly centered around the Persian Gulf region off the shores of where Friday's drone was said to have entered.
In June, Iran shot down an unmanned United States surveillance drone, which the elite Islamic Revolutionary Guard Corps (IRGC) said was flying over southern Iran - a move that brought the region to the brink of war.
Relations between Iran and the United States have worsened since past year when President Donald Trump pulled out of Tehran's 2015 nuclear deal with world powers and reimposed sanctions on the country.
Israeli Prime Minister Benjamin Netanyahu hinted in August at possible Israeli involvement in attacks on Iranian-backed militia positions in Iraq. "All U.S. equipment has been accounted for".
Iran's arch-foe Israel declined to comment on the incident.
Washington has responded with a military build-up in the Gulf and has launched an operation with its allies to protect navigation in Gulf waters.