Nikki Haley, United States ambassador to the United Nations, said Thursday she had "indisputable" evidence that Iran is violating global law.
But Mr Haley said several technical details - the absence of stabiliser fins and a series of valves on the side - marked the missile as Iranian-made.
Saudi Arabia and its allies view the Houthi rebels as an Iranian proxy on its doorstep.
Zarif, who served as Iran's representative to the United Nations from 2002 to 2007, likened the display to former Secretary of State Colin Powell's United Nations 2003 presentation meant to highlight the need to go to war with Iraq.
She said this particular missile had been manufactured in Iran, delivered to Yemen, and later fired at a commercial airport in Saudi Arabia.
"Today's revelations proved yet again that Iran's risky presence in the Middle East is only growing despite their attempts to deceive the world", Ambassador to the UN Danny Danon said in a statement.
In a presentation at the headquarters to the Defence Intelligence Agency in Washington, the U.S. envoy to the UN, Nikki Haley, said: "As you know we do not often declassify this type of military equipment recovered from these attacks but today we are taking an extraordinary step of presenting it here in an opening setting".
In a speech in a warehouse at Joint Base Anacostia-Bolling in the United States capital, Haley said the USA intelligence community has uniformly and unequivocally assessed that Iran is supplying arms to Houthi rebels in Yemen illegally, against a series of UN Security Council resolutions restricting its export of arms and missiles.
"We have said everything doesn't have to be tied to the nuclear deal, but it does have to be tied to the security council resolutions".
Iran's "ballistic missile and advanced weapons are turning up in war zones across the region".
The Iranian government issued a statement Thursday disputing Haley's claims. The statement went on: "The U.S. government has an agenda and is constantly at work to deceive the public into believing the cases they put together to advance it".
But the report does not firmly conclude that the missiles came from Iran. Dubai is next."Statements by the United Nations and U.S., as well as reports by intelligence agencies, are significant because they corroborate and substantiate what Saudi leaders have previously pointed out, that Houthi missiles targeting Riyadh were made by Iran".
The United States and Saudi Arabia accuse Iran of arming Houthi rebels in Yemen, including missiles the fired at Saudi Arabia in July and November.
Haley echoed Mattis' long-held position that the nuclear deal with Iran, in which sanctions were lifted in return for Iran's halt to its nuclear programs, should not be allowed to divert attention from Iran's other threats to USA national security interests.