Jubeir also said that all Iranian diplomats must leave Saudi Arabia within 48 hours.
Saudi Arabia “is breaking off diplomatic ties with Iran and requests that all members of the Iranian diplomatic mission leave, within 48 hours,” he told a news conference.
On Saturday, a mob attacked the Saudi embassy in Tehran and a consulate in second city Mashhad amid protests against the execution in Saudi Arabia of Sheikh Nimr al-Nimr.
The 56-year-old, a force behind 2011 anti-government protests in eastern Saudi Arabia, was among 47 convicted men put to death on Saturday in the kingdom.
The others were Shia activists and Sunnis who the Saudi interior ministry said were involved in Al Qaeda attacks, with some beheaded and others shot by firing squad.
Iran arrested 44 people over the embassy assault, which President Hassan Rouhani described as “totally unjustifiable”.
In Tehran a senior Iranian official said on Monday that Saudi Arabia’s decision to cut ties with Iran after attacks on the kingdom’s diplomatic missions in the Islamic Republic will not distract from Riyadh’s “big mistake” of executing a top Shia cleric.
“By deciding to sever (diplomatic) relations, Saudi Arabia cannot make (the world) forget its big mistake of executing a cleric,” deputy foreign minister Hossein Amir Abdollahian said, according to the IRNA agency.
He added that Saudi Arabia had committed a “strategic error in adopting rash and hasty decisions that have spread instability and caused the development of terrorism in the region”.
Riyadh’s execution of Nimr al-Nimr sparked widespread protests across Shiite-majority countries in the Middle East, with a mob attacking the Saudi embassy in Tehran and a consulate in the second city Mashhad.
The assaults on the diplomatic missions spurred the Sunni Arab kingdom to sever ties with Iran, its long-time regional rival.
In recent years, the two countries have been divided over the war in Syria, where Iran is backing the regime, and the conflict in Yemen where a Saudi-led coalition is battling Shiite rebels.
Abdollahian also said Saudi Arabia was “undermining the interests of its own people and the Muslim people of the region with its plot to bring down oil prices”, referencing crude prices that are near multi-year lows.
Iran and Saudi are major producers, but Riyadh’s current level of crude output far outpaces that of the Islamic Republic and it is seen as a heavyweight in its ability to help set the direction of oil prices.