The announcement comes after Iran admitted on Saturday that it had sent drones to Russia, but said it had done so before the Ukraine war.
The Washington Post reported on 16 October that Iran was preparing to ship missiles to Russia, but Tehran rejected the report as "completely false".
Unlike ballistic missiles, hypersonic missiles fly on a trajectory low in the atmosphere, potentially reaching targets more quickly.
North Korea's test of a hypersonic missile last year sparked concerns about a race to acquire the technology.
Russia currently leads the race to develop the missiles, followed by China and the United States.
Both Iran and Russia are targeted by stringent sanctions -- Iran after the US unilaterally pulled out of the 2015 nuclear deal between Tehran and world powers, and Russia since it invaded Ukraine in February.
The two countries have responded to the sanctions by boosting cooperation in key areas to help prop up their economies.
Stalled nuclear talks
A hypersonic missile is manoeuvrable, making it harder to track and defend against.
While countries like the United States have developed systems designed to defend against cruise and ballistic missiles, the ability to track and take down a hypersonic missile remains a question.
Thursday's announcement comes against a backdrop of stalled talks on reviving the 2015 nuclear deal.
The deal reached with six major powers -- Britain, China, France, Germany, Russia and the US -- gave Iran relief from sanctions in return for guarantees it could not develop an atomic weapon.
Iran has always denied wanting a nuclear arsenal.
The deal collapsed after the unilateral withdrawal of the United States in 2018 under then president Donald Trump.
It also follows Iran's announcement on November 5 of the successful test flight of a rocket capable of propelling satellites into space.
The United States has repeatedly voiced concern that such launches could boost Iran's ballistic missile technology, extending to the potential delivery of nuclear warheads.
In March, the US government imposed sanctions on Iran's missile-related activities.
It said in a statement at the time that the punitive measures followed "Iran's recent missile attack on Arbil, Iraq, as well as missile attacks by Iranian proxies against Saudi Arabia and the United Arab Emirates".
"These attacks are a reminder that Iran's development and proliferation of ballistic missiles pose a serious threat to regional and international security," it said.