Tension rises as Tehran accuses Saudi-led coalition of sending war planes to attack embassy in Yemen.
A spokesman for Iran's Foreign Minister, Hossein Jaber Ansari, blamed Saudi Arabia for "damage to the embassy building and the injury to some of its staff".
But residents in the capital of Sanaa said an air strike had missed the compound by 700m.
Iran and Saudi Arabia have been fighting a proxy war in Yemen for nine months, with Riyadh leading bombing raids against Iran-backed rebels who forced the country's internationally recognised President into exile in March last year.
Tensions between Iran and Saudi Arabia came to the boil last week after Riyadh announced it had executed a Shia cleric whose fate Tehran had followed closely.
Although an Associated Press reporter in Sanaa said he saw no damage to the Iranian embassy yesterday, the provocation of a nearby strike was enough to prompt further retaliation from the Iranian Government.
"The Cabinet has banned the entry of all Saudi products and products from Saudi Arabia," the Government said, noting that a ban on Iranians travelling to the Saudi holy city of Mecca for the umrah pilgrimage was also in place "until further notice".
Saudi officials could not be reached for comment on the Iranian claims. But the kingdom's Deputy Crown Prince dismissed any suggestion that the row could spill over into outright war.
"It is something that we do not foresee at all, and whoever is pushing towards that is somebody who is not in their right mind," Mohammed bin Salman, the Saudi Defence Minister and son of King Salman, told the Economist magazine.
"Because a war between Saudi Arabia and Iran is the beginning of a major catastrophe in the region. For sure we will not allow any such thing."
Human rights organisations have accused the Saudi-led coalition of indiscriminate bombing in Yemen. Almost 6000 people have been killed and schools and hospitals targeted.
The diplomatic standoff between Iran and Saudi Arabia began last weekend when the kingdom executed Sheikh Nimr al-Nimr and 46 others convicted of terror charges - the largest mass execution it has carried out since 1980.
Nimr was a staunch critic of the Saudi Government and demanded greater rights for the kingdom's Shia population, but always denied advocating violence.
In eastern Saudi Arabia, the home of Nimr and much of the kingdom's roughly 10 to 15 per cent Shia population, three days of mourning over his death ended on Thursday.
The Shia there held a memorial service - not a funeral, as the sheikh's brother has said Saudi authorities had already buried his body in an undisclosed cemetery.
There are concerns new unrest could erupt. Nimr's brother, as well as another local resident of al-Awamiya in eastern Saudi Arabia, said they'd heard gunfire on recent nights.
The local resident, who spoke to the Associated Press on condition of anonymity out of fear for her safety, shared a mobile phone video showing Saudi armoured personnel carriers moving through local streets.
Meanwhile, more protests were expected after Friday prayers, while mourners in Bahrain planned a candlelight vigil for the sheikh.
More than 1040 people were detained in Shia protests in eastern Saudi Arabia between February 2011 and August 2014, demonstrations inspired by the Arab Spring, according to Human Rights Watch.
The watchdog and other groups have alleged that Saudi officials discriminate against the Shia community by rarely allowing them to build mosques and limiting their access to public education, government employment and the justice system.
