The sites both appeared with error messages and users had been complaining on Twitter, while 40-minute outages were also reported in the US and Asia.
A hacking group appeared to claim responsibility for taking down the two services.
Facebook had 1.25 billion monthly active users at the end of September last year, while its photo-sharing service Instagram has 300 million active monthly users uploading around 70 million photos per day.
A hacking group called Lizard Squad tweeted “Facebook, Instagram, Tinder, AIM, Hipchat #offline #LizardSquad”.
Yesterday it attacked the website of Malaysia Airlines, which was offline for at least seven hours, replaced by a message from the group.
Lizard Squad has claimed responsibility for several hacks over the past year, most of them aimed at gaming or media companies.
Last year it claimed it was behind attacks on Sony’s online PlayStation network and Microsoft’s Xbox site.
Social media users who were relieved to still be able to access Twitter shared their complaints about the outage.
Scarlett Moffat, from the Channel 4 show Gogglebox, tweeted: “What Instagram and Facebook are down!! But how will I know what your morning Starbucks looks like.”
Twitter user Vince Caso said: “Livetweeting is my last comfort. It is so difficult to judge people in 140 characters. I miss Facebook.”
Fortune Feimster commented: “Facebook and Instagram are back up! Everyone can get out of their foetal position.”