Some of the white covering on the venue could be seen flapping in the strong winds in footage shared on social media.
The famous building, formerly known as the Millennium Dome, hosts major events including concerts and features restaurants, bars, shops and a cinema.
On its official Twitter account the O2 is described as: “Not just a tent. The world’s most popular music and entertainment venue.”
Visitors can also do a 90-minute climb of the recognisable roof for views of London as part of its Up at the O2 experience.
As Storm Eunice hit the city on Friday morning, witness Mala Sharma said she had seen parts of the dome damaged.
She said “more and more parts are getting ripped off”, adding “it’s going to be a safety issue for people around”.
Ms Sharma said it happened “right in front of my eyes” and the damage “started off with a patch”, but then a “chunk” of the dome roof ripped off.
Simply Red, who had been due to play the venue this weekend, but postponed due to Covid, described the damage as “tragic”.
Accompanied by a picture of the gaps in the roof, a tweet from the band’s account read: “Looks like the O2 shows wouldn’t have happened anyhow. Tragic. #Eunice”
The O2 has been contacted for comment.
Millions of people have been urged to stay at home for the day due to safety fears over the impact of Eunice, one of the worst storms to hit the UK in a generation.