Saudi Arabia is responsible for the damage to the embassy building and the injury to some of its staff," Foreign Ministry Spokesman Hossein Jaber Ansari was quoted as saying by Iranian state television news channel IRIB.
Residents and witnesses in the capital Sanaa said there was no damage to the embassy building in Hadda district.
They said an air strike had hit a public square about 700 metres (yards) away from the embassy and that some stones and shrapnel had landed in the embassy's yard.
A growing diplomatic dispute between Riyadh and Tehran triggered by Saudi's execution of a prominent Shi'ite cleric has damaged the outlook for any resolution to the conflict in Yemen,
where a coalition led by Saudi Arabia has been fighting the Shi'ite, Iran-allied Houthi movement.
A Sanaa resident went to the embassy on Thursday and reported no damage but said there was some shrapnel strewn nearby.
Saudi coalition spokesman Brigadier General Ahmed Asseri said coalition jets carried out heavy strikes in Sanaa on Wednesday night to target missile launchers used by the Houthi militia to fire at Saudi Arabia.
He said the coalition would investigate Iran's accusation and added that the Houthis has used civilian facilities including abandoned embassies.
Asseri said the coalition had requested all countries to supply it with coordinates of the location of their diplomatic missions and that accusations made on the basis of information provided by the Houthis "have no credibility".
While Riyadh sees the Houthis as a proxy for bitter regional rival Iran to expand its influence, the Houthis deny this and say they are fighting a revolution against a corrupt government and Gulf Arab powers beholden to the West.