China and Kazakhstan abstained, while Bolivia also voted against the measure.
A report in January by the United Nations panel of experts said Iran violated the 2015 arms embargo by failing "to take the necessary measures" to prevent the direct or indirect supply of missiles and drones to Shiite Houthi rebels in Yemen.
Khoshroo added that Iran rejects the U.S. false claims that Iran handed over weapons to Yemen, emphasizing that those claims are aimed at helping the aggressors.
Vassily Nebenzia, the Russian Federation ambassador, said his country could not support the UK-drafted text.
Even before Monday, the United Kingdom had been forced to water down its draft resolution condemning Iran for violating the arms embargo on Yemen. The draft pledged action against violators.
Kelley Currie, the USA representative to the United Nations, said the UK-drafted resolution was a "simple, commonsense one" which called out Iran. The embargo was due to expire at midnight on February 26.
He urged council member not to "shy away from calling out those who violate" sanctions.
Speaking before the vote, Vassily Nebenzia, the Russian ambassador, said Moscow objected to the "selective and contentious" conclusions of the panel of experts. And he warned that the resolution's adoption would have "dangerous, destabilizing ramifications" in Yemen and the region.
The US immediately lashed out at Moscow for its veto, blaming Russian Federation for shielding a "terrorist-sponsoring" Iran.
USA envoy Kelley Currie accused Russian Federation and other countries that did not support the vetoed resolution to put pressure on Iran of "deciding to shield Tehran from responsibility".
Haley did not specify what kind of action could be taken.
Russia, which has traditionally friendly relations with Iran, is providing military support along with Tehran to Syrian President Bashar al-Assad's forces.
"As a result, the panel finds that the Islamic Republic of Iran is in non-compliance with paragraph 14 of resolution 2216 (2015) in that it failed to take the necessary measures to prevent the direct or indirect supply, sale or transfer, of Borkan-2H short-range ballistic missiles, field storage tanks for liquid bi-propellant oxidizer for missiles and Ababil-T (Qasef-1) unmanned aerial vehicles, to the then Houthi-Saleh alliance".
After hours of negotiations in a bid to reach a compromise, Russian Federation made clear it had strong reservations about the findings of the United Nations report and would not support a draft resolution that mentioned them.
Yemen, the Arab world's most impoverished country with a population of 26 million, plunged into war in 2014 after the Huthis took over the capital, Sanaa, and forced the internationally recognized government to flee and seek support from neighboring Gulf Arab countries.