Iran has dismissed the accusation, reported by the Saudi Press Agency on Tuesday, as "contrary to reality". The Houthis have given warning that Saudi and UAE airports could be their next firing targets.
The Islamic Republic supports the Shia Houthi rebels but denies arming them.
However, the current crisis extends far beyond Yemen: Saudi Arabia has made clear it wants to curb Iranian influence not just in the Arabian Peninsula but across the region.
Iran has proxies across the Middle East; in Iraq, it controls paramilitary forces that are stronger than the state.
In Yemen, Saudi Arabia is in a quagmire, unable to defeat the Houthi rebels.
|Pro-Houthi Al Masirah TV has aired purported images of Saturday's missile launch [Reuters]|
Hariri has not returned to Lebanon since his announcement.
Instead, he has travelled to Abu Dhabi, a Saudi ally in the anti-Iranian camp, for talks on the escalating political crisis back home.
Saudi Arabia is at odds with the Lebanese government after backing the resignation of Hariri, but curbing Hezbollah's influence and power will not be easy.
Hezbollah is not just an armed group, but a political party with strong popular support. And in recent years, it has extended its influence beyond Lebanon's borders.
Hezbollah's decision to send troops to fight alongside Syrian President Bashar al-Assad's forces has long been an issue of concern among some Lebanese factions.
But it has strenuously resisted calls to disarm and to withdraw from Syria.
Iran has now secured a land corridor stretching from Tehran through Iraq and Syria all the way to Lebanon, a country in which Saudi Arabia hopes to change the balance of power.
It is not clear what action Saudi Arabia will take, but the kingdom, which has classified Hezbollah as a "terrorist" organisation, is now using stronger language and is threatening action.
Speaking to Al Jazeera, George Alam, a political analyst, said: "Saudi Arabia, through its threats, want the Lebanese government and people to finish off Hezbollah. It is an invitation to civil war.
"There is a new front - Saudi, Israeli and the US - against Iran."
Iranian daily warned
Against this background, Iranian media said on Tuesday the government's press supervisory board had put Kayhan newspaper on notice after it ran a headline saying Dubai was the "next target" for Yemen's Houthi rebels.
The front-page headline ran on Monday, two days after the missile fired by the Houthis was intercepted near Riyadh's international airport.
The semi-official ISNA news agency reported the supervisory board's action, saying the auditors felt the headline was contrary to Iran's interests and national security.
A Saudi-led military coalition went to war with the Houthi rebels in March 2015 after they seized the capital, Sanaa.
The Saudi-led coalition has intensified its Yemen embargo after the missile incident, which could further limit access for the delivery of humanitarian aid to the Arabian Peninsula country, which has been devastated by more than two years of conflict.
The war has killed more than 10,000 civilians, driven three million people from their homes, and left millions of Yemenis without basic necessities.
Yemen's main international airport, in the rebel-held capital, Sanaa, has been closed since August 2016 by order of the coalition.
The rebel-held north has largely relied on the Red Sea port of Hodeida, which is controlled by the Houthis, for delivery of much-needed humanitarian aid and fuel supplies.
A full blockade of the port would cut off a crucial lifeline for the Houthis, as well as millions of civilians.
|Riyadh was shaken by Saturday's missile attack by the Houthis [Faisal al-Nasser/Reuters]|