Iran blasted the decision, which follows Saudi Arabia's move to cut off diplomatic and economic relations with Iran.
"A war between Saudi Arabia and Iran is the beginning of a major catastrophe in the region, and it will reflect very strongly on the rest of the world".
Iranian protesters responded by attacking the Saudi Embassy in Tehran and its consulate in Mashhad.
An Associated Press reporter in Yemen's capital says he sees no damage at the Iranian Embassy after the Islamic Republic said it was hit in an overnight Saudi-led strike. The Shiites there held a memorial service Thursday night - not a funeral, as the sheikh's brother has said Saudi authorities had already buried his body in an undisclosed cemetery.
Iranians have rallied against Saudi Arabia to protest the kingdom putting to death Shiite cleric Sheikh Nimr al-Nimr, an execution that sparked regional protests and tensions.
They point to a series of steps Riyadh had taken in recent months towards a thaw with Tehran, including working hard to get a new ambassador approved in Iran after a months-long hiatus, opening a new embassy in Shi'ite-ruled Iraq, and sitting opposite Iran at Syria peace talks last month in NY.
Salman, the sixth brother to rule as king since 1953, has set in motion the first transfer of power to a new generation for six decades, appointing his nephew Mohammed bin Nayef as crown prince and his own son Mohammed bin Salman as deputy.
Despite these provocations, Zarif said Iran has refused to retaliate or even downgrade diplomatic relations with Saudi Arabia.
Saudi Arabia severed ties with Iran on Sunday after crowds of protesters attacked two of its diplomatic posts in Iran.
Iran has accused the Sunni Muslim monarchy of Saudi Arabia of using the attack on the embassy as an "excuse" to sever ties and further increase sectarian tensions. The watchdog and other groups have alleged that Saudi officials discriminate against the Shiites by rarely allowing them to build mosques and limiting their access to public education, government employment and the justice system. Egypt, Jordan, Morocco and Sudan have joined in the military campaign.
Saudi Arabia announced the execution of Sheikh Nimr and 46 others on Saturday despite global calls for the release of the opposition cleric and other jailed political activists in the kingdom.
Trade between Saudi Arabia and Iran is small compared with the size of their economies, but tens of thousands of Iranians travel to the kingdom every year to complete the haj as well as Umrah pilgrimages made outside of haj season.
