BA took the officials' advice and decided to stop flying to the Saudi cities of Riyadh and Jeddah.
The airline usually flies to both cities four times a week.
Quite a lot of British people work in Saudi and they're being told about what's happened.
The Government has already warned people not to travel to the country unless they have to.
Saudi Arabia is where September 11 attacks suspect Osama Bin Laden comes from.
He's the head of the terror group al-Qaeda.
It's not known who's behind the threats which have led to the British Airways flights being grounded.