British Prime Minister Theresa May said the incident was being treated as a terrorist attack. If confirmed, it would be the deadliest militant assault in Britain since four al-Qaeda-linked people killed 52 people in suicide bombings on London's transport system in July 2005.
Police responded to reports of an explosion shortly after 10:35 pm (2135 GMT) at the arena, which has the capacity to hold 21,000 people, where US singer Ariana Grande had been performing to an audience that included many children, Reuters reported.
A witness who attended the concert said she felt a huge blast as she was leaving the arena, followed by screaming and a rush by thousands of people trying to escape the building.
A video posted on Twitter showed fans, many of them young, screaming and running from the venue. Dozens of parents frantically searched for their children, posting photos and pleading for information on social media.
"We were making our way out and when we were right by the door there was a massive explosion and everybody was screaming," concert-goer Catherine Macfarlane told Reuters.
"It was a huge explosion - you could feel it in your chest. It was chaotic. Everybody was running and screaming and just trying to get out."
May will hold a crisis response meeting on Tuesday.
Manchester Chief Constable Ian Hopkins said police were treating the blast as a terrorist incident and were working with counter-terrorism police and intelligence agencies but gave no further details on their investigation.
There was no immediate claim of responsibility.