ISIS claimed responsibility for attack, saying, "One of the soldiers of the Caliphate was able to place an explosive device within a gathering of the Crusaders in the city of Manchester."
Prime Minister Theresa May called an emergency meeting with intelligence chiefs on the deadliest militant assault in Britain since four British Muslims killed 52 people in suicide bombings on London's transport system in July 2005.
Witnesses related the horror of the blast which prompted a stampede just as the concert ended at Europe's largest indoor arena.
"We ran and people were screaming around us and pushing on the stairs to go outside and people were falling down, girls were crying, and we saw these women being treated by paramedics having open wounds on their legs ... it was just chaos," said Sebastian Diaz, 19.
"It was literally just a minute after it ended, the lights came on and the bomb went off," Diaz said.
Police responded to reports of an explosion shortly after 10:33pm at the arena, which has the capacity to hold 21,000 people, where the US singer had been performing to an audience that included many children.
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."
Ariana Grande, 23, later said on Twitter: "broken. from the bottom of my heart, i am so so sorry. i don't have words."
May, who faces an election in two-and-a-half weeks, said her thoughts were with the victims and their families. Her ruling Conservative Party was preparing to suspend campaigning ahead of the election due to the suspected attack.
"We are working to establish the full details of what is being treated by the police as an appalling terrorist attack," she said in a statement. "All our thoughts are with the victims and the families of those who have been affected."
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.
US President Donald Trump described the attack as the work of "evil losers". German Chancellor Angela Merkel said it "will only strengthen our resolve to...work together with our British friends against those who plan and carry out such inhumane deeds."
London Mayor Sadiq Khan said more police had been ordered onto the streets of the British capital. London's Victoria coach station was briefly closed after discovery of a suspect package.
A source with knowledge of the situation said the bomber's explosives were packed with metal and bolts. At least 19 of those wounded were in a critical condition, the source said.
There was no immediate claim of responsibility, but US officials drew parallels to the coordinated attacks in November 2015 by Islamist militants on the Bataclan concert hall and other sites in Paris, which claimed about 130 lives.
Two US officials who spoke on condition of anonymity said that initial signs pointed to a suicide bomber being responsible for the blast.
"In the absence of conclusive evidence, the choice of venue, the timing and the mode of attack all suggest this was terrorism," said a US counter terrorism official who also spoke on condition of anonymity.
Islamic State supporters took to social media to celebrate the blast and some encouraged similar attacks elsewhere.
Britain is on its second-highest alert level of "severe", meaning an attack by militants is considered highly likely.
The US Department of Homeland Security was monitoring the situation in Manchester closely but said it had no information to indicate a specific credible threat involving music venues in the United States.
British counter-terrorism police have said they are making on average an arrest every day in connection with suspected terrorism.
In March, a British-born convert to Islam ploughed a car into pedestrians on London's Westminster Bridge, killing four people before stabbing to death a police officer who was on the grounds of parliament. The man was shot dead at the scene.
In 2015, Pakistani student Abid Naseer was convicted in a US court of conspiring with al Qaeda to blow up the Arndale shopping centre in the centre of Manchester in April 2009.