The BBC reports residents in the city said there had been dozens of air strikes in the morning of 7 January. The Saudi-led coalition is battling Houthi rebels in Yemen, who Riyadh claims are backed by Iran.
An AP reporter at the scene claims there is no visible damage to the embassy structure.
Coalition spokesman Brigadier General Ahmed Asseri told Reuters it was investigating claims that its missiles had hit the Iranian embassy but said it had the coordinates of all diplomatic missions in the city, and implied Iran’s accusation was based on information from Houthi sources “who have no credibility”.
The alleged missile strike comes amid escalating tensions between Saudi Arabia and Iran following the execution of Shia dissident cleric Nimr al-Nimr by the Saudis.