The US government has released images which it says shows the damage by drones in Saturday's attack.
The state-owned oil company Saudi Aramco says it lost six million barrels of oil - which would affect six percent of the world's oil output.
However, Saudi Arabia's energy minister says it has stockpiles of oil which will be used to offset the loss of production.
But oil markets haven't seen a shutdown on this scale since Iraqi troops invaded Kuwait to start the first Gulf War in 1990 - and it's not clear how long repairs will take.
Al Jazeera's Scheherazade Gaffoor reports.