A resolution needs nine votes in favor and no vetoes by Russia, China, the United States, France or Britain to pass.
The United Nations Security Council will meet on Monday to renew its targeted sanctions on Yemen.
The U.S. has been lobbying for months for Iran to be held accountable at the United Nations for violating an arms embargo on Houthi leaders.
It also claimed that these missiles were used to launch an attack on neighbouring Saudi Arabia - which along with several Sunni Arab countries - have been fighting against the Houthis since March 2015 when the Kingdom intervened to push back the rebels and reinstate the government of President Abd-Rabbu Mansour Hadi. The former gained 11 favorable votes, while Russian Federation and Bolivia voted down the draft resolution, and two countries - Kazakhstan and China - abstained.
Russia's Representative to the United Nations welcomed the unanimous passage of the resolution and thanked the Council's delegation for "making a correct decision". Meanwhile, the British text contained condemnations against Tehran, which western countries suspect of illegal supplies of weapons to Yemeni rebels.
"We can not concur with uncorroborated conclusions and evidence which requires verification and discussions within the sanctions committee", Russian Ambassador Vassily Nebenzia told the council.
The British-drafted resolution against Iran at the UN Security Council over the Yemen conflict would be helping the "aggressors", Foreign Ministry spokesman Bahram Qassemi said on Monday, slamming the British government for its "dishonest" behavior.
The report by a United Nations panel of experts concluded that Iran was in violation of the 2015 arms embargo after determining that missiles fired by the Houthis at Saudi Arabia a year ago were made in Iran.
The US immediately lashed out at Moscow for its veto, blaming Russian Federation for shielding a "terrorist-sponsoring" Iran.
After the Russian veto, US Ambassador Nikki Haley repeated her anti-Russian and anti-Iranian remarks, accusing Russia of protecting "the terrorist-sponsoring regime in Iran" and warned of further action targeting Iran, AFP reported.
Russian envoy to the UN Vasily Nebenzia welcomed the Security Council's unanimous support of the Russian resolution.
Instead, the UNSC unanimously adopted a Russian-proposed resolution that did not mention Iran.
An alarming 17 million people in Yemen - 60 percent of the total population - are in need of food aid, of whom seven million are on the brink of starvation because of the conflict, according to the United Nations.
Iran has repeatedly denied arming Yemen revolutionaries, stressing that such accusations have been baseless, and lashing out at the worldwide community for Turing a blind eye on the USA and Britain for selling Saudi Arabia arms that could be used to commit war crimes in the Arab impoverished country.
Iran has accused Washington of "participation and responsibility" for what it says are "atrocities committed by Saudi Arabia in Yemen".
Haley did not specify what kind of action could be taken.