Oil prices rose Tuesday, with benchmark Brent crude trading over $71 a barrel, up more than $1 on the day.
However, Al-Falih stressed that the production and exports of Saudi crude oil and products will continue "without interruption".
Two oil tankers belonging to the Saudi national shipping company in the Red Sea were attacked by Yemen's Houthi militia after crossing the Bab al-Mandab Strait in 2018 as well. It wasn't immediately known where the Houthis launched the drones. This latest development is ratcheting up tensions in the already troubled region. The attack caused fire and minor damage to one of the pumping stations, Falih said.
The attacks targeted two oil pump stations on the East-West Pipeline, which carries oil from Saudi Arabia's Eastern Province to the Port of Yanbu, the Saudi Press Agency reported. It added that Saudi Aramco's oil and gas supplies have not been affected by the attack.
Meanwhile, the details around alleged acts of sabotage to four oil tankers, including two belonging to Saudi Arabia, off the coast of the UAE's port of Fujairah remain unclear.
An Emirati official said three Western countries - the US, France and Norway - would be part of an investigation into the ship attacks along with the UAE and Saudi Arabia.
He added that the UAE has handed a letter to the security council on the sabotage of the oil tankers. The other three showed no visible damage from above.
Iran, using regional proxies, has been gradually scaling up its attacks against Saudi oil targets since 2003.
Washington's dispatch to the region of the USS Abraham Lincoln carrier group, an amphibious assault ship, a Patriot missile battery and B-52 bombers has sparked fears of possible military clashes.
Iranian officials have said that they could reach 20% enrichment within four days.
The United Nations urged restraint from all sides.
Washington and its Gulf allies stopped short of blaming Riyadh's regional arch-rival Tehran for the sabotage, but US President Donald Trump warned Iran against doing anything to harm US interests.
For his part, US president Donald Trump said he expects to speak to Chinese president Xi Jinping at a G20 summit in late June and have "probably a very fruitful meeting". Today's drone strike showed Saudi Arabia's second supply line was also vulnerable.