Demonstrators broke into the embassy and started fires before being cleared away by the police, Iran's ISNA news agency reported, after gathering there to denounce the kingdom for executing a prominent Shi'ite cleric on Saturday.
Video shows protesters inside Saudi embassy in Tehran pic.twitter.com/DEmsNLI6ZG — Sobhan Hassanvand (@Hassanvand) January 2, 2016
The ministry issued a statement early on Sunday calling on protesters to respect the diplomatic premises, according to the Entekhab news website.
There have been protests around the world following the execution of Shia cleric, Sheikh Nimr al-Nimr in Saudi Arabia.
The prominent and outspoken cleric of the Saudi government was among 47 people executed after being convicted of terrorism offences.
He was a supporter of mass protests in the province in 2011. His brother, Mohammed al-Nimr rejects the terrorism charges saying he never advocated violence.

Iranian protesters gather outside the Saudi Embassy in Tehran during a demonstration against the execution of Nimr al-Nimr Source: Getty Images
"The first thing is that most of the charges levelled against the cleric al-Nimr are not true. Even if all the charges included in the verdict were true it shouldn't have reached the level of execution or killing. So we regard this execution as a political execution."
Iran, the main rival of Sunni-ruled Saudi Arabia said the Kingdom would pay a heavy price for the exection, and accused the Saudi's of supporting dissent abroad while suppressing it at home.
Lebanon's Supreme Islamic Shi'ite Council has condemned the execution of a prominent , saying it was a "grave mistake".
The execution of the sheikh has raised fears that his nephew Ali al-Nimr, who was 17 when he was arrested, could also have the death sentence imposed on him carried out.
Saudi authorities send message to militants
The executions seemed mostly aimed at discouraging Saudis from jihadism after bombings and shootings by Sunni militants in Saudi Arabia over the past year killed dozens and Islamic State called on followers there to stage attacks.
After the executions, Islamic State urged its supporters to attack Saudi soldiers and police in revenge, in a message on Telegram, an encrypted messaging service used by the group's backers, the SITE monitoring group reported.
Saudi Arabia's ruling Al Saud family has grown increasingly worried in recent years as Middle East turmoil, especially in Syria and Iraq, has empowered Sunni militants seeking to bring it down and given room to Iran to spread its influence. A nuclear deal with Iran backed by Saudi Arabia's biggest ally, the United States, has done little to calm nerves in Riyadh.
But Saudi Arabia's Western allies, many of whom supply it with arms, are growing concerned about its new assertiveness.
EU foreign policy chief Federica Mogherini said Nimr's execution risked "dangerous consequences" by further inflaming sectarian tensions in the region, and a German Foreign Ministry official said it "strengthens our existing concerns about increasing tensions and deepening rifts in the region".
The simultaneous execution of 47 people - 45 Saudis, one Egyptian and a man from Chad - was the biggest mass execution for security offences in Saudi Arabia since the 1980 killing of 63 jihadist rebels who seized Mecca's Grand Mosque in 1979.
The 43 Sunni jihadists executed on Saturday, including several prominent al Qaeda leaders and ideologues, were convicted for attacks on Western compounds, government buildings and diplomatic missions that killed hundreds from 2003-06.
The four Shi'ites were convicted of involvement in shootings and petrol bomb attacks that killed several police during anti-government protests from 2011-13 in which over 20 members of the minority sect were also shot dead by the authorities.
Under Saudi Arabia's reading of Islamic law, such attacks are interpreted as "banditry", carrying an automatic sentence of death followed by public display of bodies on gibbets.
Grand Mufti Abdulaziz Al al-Sheikh, the kingdom's top religious authority, praised the executions as "just".