The geopolitical uncertainty has pushed up flagging oil prices, as analysts speculate over restricted production.
Benchmark Brent crude futures were up 76 cents on the day at $38.04 a barrel at 1115 GMT, near an intraday high of $38.50, Reuters reported.
Tehran intends to boost oil production when sanctions against it come to an end, which some analysts attribute to the price not rising any higher over the international tension.
Iranian diplomatic personnel, meanwhile, have 48 hours to leave Saudi Arabia, Foreign Minister Adel al-Jubeir said late on Sunday.
Saudi diplomats in Iran have also been called home.
"Iran's history is full of negative interference and hostility in Arab issues, and it is always accompanied by destruction," Jubeir said at a news conference on Sunday.
The standoff is the latest turmoil in often fractious Saudi-Iranian relations that last saw diplomatic ties severed between 1988 and 1991.
The breaking of diplomatic ties is an attempt by Riyadh to divert attention from its domestic problems, said Iran's Foreign Minister Spokesman Hossein Jaberi Ansar on Monday.
"It seems that Saudi Arabia considers not only its interest, [but also] its survival in the continuation of tensions and conflicts and is trying to settle its domestic problems through blame games," Ansari said during his weekly press conference in the Iranian capital, Tehran.
Bahrain, a staunch Saudi ally and fellow oil producer, has also severed relations with Tehran, giving Iranian diplomats 48 hours to leave the island country.
Sudan, which had already tense relations with Iran over Tehran's support of Houthi rebels in Yemen, has also given the Iranian ambassador the boot from Khartoum.
The United Arab Emirates is also reducing its diplomatic presence in Tehran, and has reportedly asked Iran to withdraw many of its foreign office staff from Abu Dhabi.
|Read more: Iranian-Saudi tensions at boiling point over outspoken cleric's execution|
Tensions erupted following the execution of Nimr al-Nimr, a leading Saudi Shia cleric and activist. His nephew, Ali Mohammed al-Nimr - whose case made international headlines after he was condemned to death despite being only 17 at the time of his arrest - remains on death row.
Iran's supreme leader Ali Khamenei said that Riyadh would face "divine revenge" for executing Nimr. Protests outside the Saudi embassy in Tehran have been seen daily since the execution.
Iranian protesters ransacked the Saudi embassy, as well as a consulate in the city of Mashhad on Saturday, smashing windows and setting fires to parts of the buildings.
A number of arrests were made by Iranian police.
Nimr was a vocal critic of the Saudi regime and was seen as a key figure among young Shia activists. He was convicted on terrorism charges, but denied advocating violence.
The Saudi authorities have refused to hand over Nimr's body to his family, who were told that he has been buried in an undisclosed cemetery. The ambiguity over his final resting place could lead to further protests, analysts fear.
Relations between Saudi Arabia and Iran have become increasingly hostile in recent decades as both countries vie for dominance in the Middle East and the wider Islamic world.
The conflict is being increasingly cast in a sectarian hue with Saudi and Iranian officials positioning themselves as leaders of the Sunni and Shia worlds respectively.
The rivalry between Riyadh and Tehran has found the rival governments supporting opposing groups in Lebanon, Syria and the Yemen, amid fears that the current escalation could destabilise the Middle East even further.