"We protested and complained through diplomatic, legal and political channels, especially through the UN mechanism, regarding this provocative US action", ministry spokesman Abbas Mousavi told Iran's IRIB state broadcaster.
At the same time, Iranian Foreign Minister Mohammad Javad Zarif took to Twitter to condemn the US and say that Washington was lying about its drone being hit by Iran in international waters.
"The US wages #EconomicTerrorism on Iran, has conducted covert action against us & now encroaches on our territory. We don't seek war, but will zealously defend our skies, land & waters. We'll take this new aggression to #UN & show that the US is lying about international waters," according to a tweet.
The announcements come after US President Donald Trump said in a statement that Iran has made a very big mistake by shooting down a US Navy drone.
The Islamic Revolutionary Guard Corps (IRGC) reported earlier in the day that the Iranian military had shot down a US drone in the southern part of the country after it violated Iranian airspace.
The US Central Command (CENTCOM) later confirmed that a US Navy drone was shot down by an Iranian surface-to-air missile system while operating in international airspace over the Strait of Hormuz on 19 June.
Tensions in the Gulf have escalated over the past weeks as a number of oil tankers from various nations have been attacked there and in the neighbouring Gulf of Oman. The United States and its regional allies claimed that Iran had a role in the incidents, while Tehran has denied the allegations.
In one of its recent claims voiced last week, Washington stated the IRGC allegedly tried to down one of its drones prior to attacking the vessels in the Gulf of Oman but the missile failed to hit its target.