But a reporter for the Associated Press news agency said there was no visible damage to the embassy building, which is in a neighbourhood that has previously been targeted in air strikes.
Following the Saudi government's announcement that it had executed 47 prisoners including al-Nimr, the US State Department did two things.
A scheduled January 18 trip by Defence Minister Khawaja Asif to Tehran, according to a diplomatic source, has become uncertain following the tiff between Saudi Arabia and Iran.
Performing the hajj at least once in one's life is mandatory for all Muslims who are physically and financially able to make the journey, but Iranians officials say it can still be suspended under exceptional circumstances.
Fellow Gulf Co-operation Council member Bahrain followed suit, while the United Arab Emirates downgraded its ties and Kuwait recalled its envoy. Late Sunday, Saudi Arabia announced it was severing relations with Iran because of the assaults. Iran, the region's largest Shiite power, supports Assad and the Shiite Houthi rebels who have ousted the elected government in Yemen.
"This deliberate action by Saudi Arabia is a violation of all worldwide conventions that protect diplomatic missions", foreign ministry spokesperson Hossein Jaber Ansari was quoted as saying by state television.
Oman stressed the "need to find new rules that prohibit any form of interference in the internal affairs of other countries".
After Iranian demonstrators stormed Tehran's Saudi embassy in protest, Saudi Arabia cut all ties with Iran.
The Swiss move comes after Saudi Arabia on Saturday executed Shiite cleric Nimr al-Nimr and 46 others. Iran's annual imports from Saudi Arabia total about $60 million a year and consisted mostly of packing materials and textiles.
Media reports said his counterpart from Oman, which has often played a mediating role in the region, was also expected in the Iranian capital on Wednesday.
Diplomatic relations between Saudi Arabia and Iran - Pakistan's neighbour to the west - deteriorated as Iranian protestors reacted with fury to Riyadh's execution of prominent Shia cleric Sheikh Nimr al-Nimr earlier this week.
A spokesmen for the White House insisted that the United States was not taking a side, and that Kerry was set to call Saudi Foreign Minister Adel al-Jubeir.