Iran said it would protest to the United Nations Security Council after it accused Saudi warplanes of deliberately bombing its embassy in the Yemeni capital, Sanaa.

"During an air raid by Saudi Arabia against Sanaa, a rocket fell near our embassy and unfortunately one of our guards was seriously wounded," Iranian Deputy Foreign Minister Hossein Amir Abdollahian said.

"We will inform the Security Council of the details of this attack within several hours," he said.

Often at loggerheads over regional issues, a full-blown split between Sunni-majority Saudi Arabia and Shia-dominated Iran erupted at the weekend when Riyadh executed prominent Shia cleric and activist Nimr al-Nimr along with 46 others.

Mr Nimr's death sparked demonstrations in many countries including Iran, where protesters stormed and set fire to the Saudi embassy in Tehran as well as the kingdom's consulate in second city Mashhad.

Riyadh cut ties with Tehran in response and was joined by some of its Sunni Arab allies including Bahrain and Sudan.

The United Arab Emirates also downgraded relations with Iran while Kuwait and Qatar recalled their ambassadors.

A Saudi-led coalition has waged an air war on Iran-backed rebels in Yemen since March and the impoverished nation's conflict is one of the main sources of dispute between the two regional adversaries. 

Also today, Iran banned all products from Saudi Arabia and said a ban on Iranians travelling to the Saudi holy city of Mecca for the umrah pilgrimage would remain in place "until further notice".

"The cabinet has banned the entry of all Saudi products and products from Saudi Arabia," a government statement said.