Yemen's Houthi rebels have claimed responsibility for firing the projectile on Saturday
, which was intercepted by Saudi defense forces before it hit the ground. Saudi Arabia and its Gulf allies accuse Iran of providing material support to the rebels.
"It was an Iranian missile, launched by Hezbollah, from territory occupied by the Houthis in Yemen," al-Jubeir told CNN, referring to Shia militias in Lebanon and Yemen closely allied to Tehran.
"We see this as an act of war," he said. "Iran can not lob missiles at Saudi cities and towns and expect us not to take steps," he added, citing article 51 of the UN Charter whereby a nation can act if an armed attack occurs against it.
Al-Jubeir said the missile was made in Iran and smuggled in parts into Yemen, where he claimed "operatives from the Iranian Revolutionary Guards and Hezbollah" helped put it back together again and then launch it.
"We reserve the right to respond in the appropriate manner at the appropriate time," said the softly-spoken career diplomat.
He declined to say what those measures against Iran might be.
"This is a very, very hostile act," he said. "We have been extending our hand to Iran since 1979 in friendship, and what we get back is death and destruction."
Earlier Monday, Iranian Foreign Ministry spokesman Bahram Qassemi described Saudi claims about Tehran's involvement as "false, irresponsible, destructive and provocative," the Iranian news agency Tasnim reported.
CNN spoke to al-Jubeir -- who was the Saudi ambassador to the United States before becoming Foreign Minister -- after an extraordinary series of events at the weekend
that began with the resignation of the Lebanese Prime Minister
from the Saudi capital and ended with the detainment of a large group of high-profile Saudi princes
and ministers on corruption charges, along with other officials and prominent businessmen.
Saudi to close ports and borders with Yemen
Al-Jubeir said Iran could not just "sit there" and expect to get "a free pass" to meddle in countries in the region, citing Lebanon, Yemen, Syria, Iraq and Bahrain.
He added that Saturday's missile was similar to one fired from Yemen in July that was shot down close to the Saudi city of Mecca, a month before the annual Hajj pilgrimage to Islam's holiest site.
Al-Jubeir confirmed to CNN on Monday that his country was closing its ports and borders with Yemen to stop Iranian penetration of the Kingdom.
He insisted however that humanitarian aid would still make it through to the millions of people suffering from malnutrition and cholera brought on by the years-long proxy war between the Iran-backed Houthi rebels and Saudi Arabia.
"Our objective is to increase the flow of humanitarian assistance in Yemen, but do it in such a way that Iran and its militias and its proxies cannot use that access in order to smuggle weapons and technology that can be re-assembled into missiles in Yemen, that will then be used against us and against the Yemeni people," he said.
Al-Jubeir: Hezbollah calling shots in Lebanon
With regard to Hariri's bombshell resignation Saturday, al-Jubeir said: "It is very clear that Hezbollah is undercutting him at every turn, that it is doing Iran's bidding, that the Lebanese political system became paralyzed, that the issue of a government that could act independently was a sham, it was Hezbollah who were calling the shots, and he basically said enough is enough."
The Saudi Foreign Minister said that as a dual passport holder with both Saudi and Lebanese citizenship, Hariri would be able to leave the Kingdom if he so chooses.
Lebanon's Interior Minister said Monday he expected Hariri to return in a few days.
Saudi Arabia's 'zero tolerance policy' on corruption
Al-Jubeir also described as "nonsense" speculation that Saturday's shock arrests of princes and ministers on corruption charges amounted to a grab for power and a purge of opponents by Crown Prince Mohammed bin Salman.
The Kingdom has a "zero tolerance policy on terrorism" and now, also "a zero tolerance policy on corruption," al-Jubeir said. "I assure you that the Kingdom of Saudi Arabia takes very, very seriously the issue of corruption, waste, and mismanagement."
"There is a reason why everybody was brought in or detained and will be questioned and will be investigated and these have to do with the commission. I'm sure when the investigations are complete that people will know what the reasons are."
Al-Jubeir said the arrests were in line with the Kingdom's plans to diversify the economy and modernize society by 2030 and achieve economic growth, rejecting suggestions that the detentions could put off potential investors.
"We want investors to have confidence in our system," he said. "We want companies to know that when they come to compete in Saudi Arabia they will compete fair and square with any other company and not be subject to people using their influence or their position in order to extract better deals."