In October, Iran tested a precision-guided ballistic missile capable of delivering a nuclear warhead, in defiance of a UN ban.
The US move came after global economic sanctions on Iran were lifted in line with a deal on its nuclear programme.
The new sanctions prevent 11 entities and individuals linked to the programme from using the US banking system.
Announcing the measures, Adam J Szubin, US acting under-secretary for terrorism and financial intelligence, said: "Iran`s ballistic missile programme poses a significant threat to regional and global security, and it will continue to be subject to international sanctions."
However, Iranian foreign ministry spokesman Hossein Jaber Ansari said on Monday: "Iran`s missile programme has never been designed to be capable of carrying nuclear weapons."
He said: "The US sanctions against Iran`s ballistic missile programme... have no legal or moral legitimacy."
Mr Ansari added: "America sells tens of billions of dollars of weaponry each year to countries in the region. These weapons are used in war crimes against Palestinian, Lebanese and most recently Yemeni citizens."
A UN resolution endorsing the 2015 nuclear agreement between Iran and world powers calls on Iran to refrain from testing missiles designed to carry nuclear weapons.
The new US move came just a day after sanctions against Iran were lifted over its nuclear programme. The International Atomic Energy Agency (IAEA) said it had verified that Iran had restricted its sensitive nuclear activities.
Four American-Iranians in Iran and seven Iranians in the US were also freed in a prisoner swap deal on the day sanctions were lifted.
The US had threatened to impose the missile test sanctions earlier but US sources said they were delayed as Washington did not want to undermine the nuclear deal negotiations - particularly over the prisoner swap.
The sanctions were announced only after a plane carrying the released prisoners had left Iran. President Barack Obama hailed the nuclear deal as "smart".
"Once again, we`re seeing what`s possible with international diplomacy," he said. But he said the US would "remain steadfast in opposing Iran`s destabilising behaviour elsewhere" - such as its missile tests.
Iranian President Hassan Rouhani said on Sunday of the new sanctions: "Any action will be met by a reaction."
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