Witnesses estimated the crowd numbered 400 at the demonstration, which went ahead without official authorisation.
The protesters shouted slogans hostile to Saudi Arabia, King Salman and the ruling royal family, calling on Iranian authorities to close the mission, Fars news agency reported.
Security forces deployed in force to protect staff at the embassy in a diplomatic quarter of northeast Tehran.
Apart from Yemen, regional rivals Saudi Arabia and Iran are also on opposite sides on the conflict in Syria, where Tehran supports President Bashar al-Assad and Riyadh backs rebels fighting for his ouster.
Iran has rejected accusations of arming the rebels and the Islamic republic's supreme leader Ayatollah Ali Khamenei has condemned the coalition air strikes as "criminal acts".
Hundreds of people also took part in a protest outside the Saudi embassy on Saturday over an alleged attempt by Saudi police to sexually assault two teenage Iranian boys.