The Saudi-led coalition combating Iran-backed Shiite rebels in Yemen denied the accusation, saying no operations were carried out near the mission.
Shiite-dominated Iran also announced a ban on imports from its Sunni-ruled rival.
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Tehran said an unspecified number of embassy staff had been wounded in the raid on the rebel-held Yemeni capital Sanaa, which has been targeted by months of coalition air strikes.
"This deliberate action by Saudi Arabia is a violation of all international conventions that protect diplomatic missions," foreign ministry spokesman Hossein Jaber Ansari said, quoted by state television.
"The Saudi government is responsible for the damage caused and for the situation of members of staff who were injured," Ansari added, without specifying when the alleged strike took place or the seriousness of the injuries.
"The Islamic republic reserves the right to pursue its interests in this matter," he said.
Later, Deputy Foreign Minister Hossein Amir Abdollahian said that "during an air raid by Saudi Arabia against Sanaa, a rocket fell near our embassy and unfortunately one of our guards was seriously wounded".
"We will inform the Security Council of the details of this attack within several hours," he said, adding that "Saudi Arabia is responsible for the security of our diplomats and of our embassy in Sanaa".
But the coalition said an investigation showed that the "allegations are false".
It added: "No operations were carried out around the embassy or near to it... The embassy building is safe and has not been damaged."
Iran also announced that a ban on Iranians travelling to the Saudi holy city of Mecca for the year-round minor pilgrimage, known as the umrah, would remain in place indefinitely.
Longstanding frictions between the Middle East's foremost Sunni and Shiite Muslim powers exploded into a full-blown diplomatic crisis at the weekend when Riyadh executed Shiite cleric and activist Nimr al-Nimr.
Nimr's death unleashed a wave of anger across the Shiite world, and protesters in Iran stormed and set fire to the Saudi embassy in Tehran and consulate in second city of Mashhad.
Iran denounced those attacks, but the repercussions quickly rippled across the region with Saudi allies Bahrain, Sudan and Djibouti also cutting diplomatic ties with Tehran.
Somalia followed suit today, saying it had given Iranian diplomats 72 hours to leave.
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