Saudi Arabia's breach of ties with Iran will extend to cutting air traffic between the countries, ending commercial relations and barring its citizens from travel to the Islamic Republic, Saudi Foreign Minister Adel al-Jubeir said.
Iranian pilgrims will still be welcome to visit Mecca and Medina, Mr Jubeir said, adding that Iran must behave like "a normal country" instead of "a revolution" and respect international norms before ties could be restored.
Saudi Arabia's Sunni allies rallied behind the kingdom and several joined Riyadh in severing or downgrading diplomatic relations with Tehran.
Bahrain and Sudan cut all ties with Iran, and the United Arab Emirates (UAE), home to hundreds of thousands of Iranians, downgraded its relations.
Saudi Arabia broke off relations yesterday after a mob stormed its embassy in Tehran.
Iran accused Saudi Arabia of using the attack on the embassy as an "excuse" to sever ties and further increase sectarian tensions, after Shias across the world denounced Saudi Arabia's execution of Shia cleric Nimr al-Nimr.
Demonstrators took to the streets of Tehran for a third consecutive day of protests over the execution of Sheikh Nimr.
Some 3,000 demonstrators gathered in Imam Hossein Square in eastern Tehran, chanting slogans against Saudi Arabia's Al-Saud royal family.
A man was shot dead in Saudi Arabia's Eastern Province last night and, and two Sunni mosques in Iraq's Shia-majority Hilla province were bombed.
Saudi Arabia executed Nimr and three other Shias on terrorism charges on Saturday, alongside dozens of Sunni jihadists.
Iran hailed him as a "martyr" and warned Saudi Arabia's ruling Al Saud family of "divine revenge".
Bahrain accused Iran of "blatant and dangerous interference" in the affairs of the Gulf Arab countries, in a statement announcing the severing of diplomatic ties.
The Yemeni government announced a curfew in the port city of Aden, a beachhead for Saudi and UAE forces waging war on the Shia Houthi group that controls much of the country.
A ceasefire collapsed on Saturday.
Saudi Arabia has defeneded its judicial process at the United Nations, saying the 47 people executed had been granted "fair and just trials without any consideration to their intellectual, racial or sectarian affiliation."
US, UN urge calm and de-escalation
The US Secretary of State has called the Iranian and Saudi foreign ministers to urge calm following the breakdown in relations.
A US official told AFP that Mr Kerry reached out to Mr Jubeir and his Iranian counterpart, Mohammad Javad Zarif, to urge "calm and de-escalation."
The United States, traditionally a much closer partner of Saudi Arabia, has no formal diplomatic relations with Iran.
However, it has been developing a closer working relationship since signing a deal to limit Tehran's nuclear ambitions in July last year.
The US is keen to avoid an escalation in tensions with Iran as it works to oversee implementation of that deal and also as it encourages Iran to play a role in peace talks to end the Syria civil war.
Meanwhile, the UN peace envoy for Syria is travelling to Saudi ahead of a visit to Iran for talks aimed at defusing tensions.
Staffan de Mistura is due to arrive in Riyadh later amid fears that the furore could undermine international peace efforts in Syria.
The UN Secretary-General, Ban Ki-moon, has told Mr Jubeir the decision to break off diplomatic ties was "deeply worrying".
Mr Ban also spoke to Mr Zarif, urging both men to "avoid any actions that could further exacerbate the situation".