The teenager, believed to have been 18, was studying health and social care at Runshaw College in Leyland, Lancashire.
In a statement in Downing Street, the prime minister said it was “now beyond doubt that the people of Manchester and of this country have fallen victim to a callous terrorist attack” that targeted “defenceless young people”.
She said the security services believe they know the attacker’s identity but are not yet able to confirm it.
It is the worst terrorist attack in the UK since the 7 July bombings in 2005 in which 52 people were killed by four suicide bombers.
So-called Islamic State has said it was behind the attack, via IS channels on the messaging app Telegram.
Sixty ambulances went to Manchester Arena after the attack and those wounded are being treated at eight hospitals around the city.
Relatives are using social media to hunt for missing loved ones, and an emergency number – 0161 856 9400 – has been set up.
Greater Manchester Police Chief Constable Ian Hopkins said it was “the most horrific incident” the city had ever faced, and the “fast-moving investigation” was now working to establish whether the attacker “was acting alone or as part of a network”.
In other developments:
The explosion happened shortly after Ariana Grande left the stage and afterwards the 23-year-old actress-turned-singer, tweeted: “broken. from the bottom of my heart, i am so so sorry. i don’t have words”
Police have established a help centre at Manchester City’s Etihad Stadium, access Gate 11, for anyone who needs assistance in tracing loved ones
The Queen has expressed her “deepest sympathy” with all those affected, adding that “the whole nation has been shocked by the death and injury”
The Arndale shopping centre in Manchester was briefly evacuated earlier, but has now reopened. A man has been arrested in connection with an incident there
Andy Holey, who had gone to the arena to pick up his wife and daughter, said: “An explosion went off and it threw me about 30ft from one set of doors to the other set of doors.”
Emma Johnson, who went to pick up her children, aged 15 and 17, told BBC Radio Manchester: “The whole building shook. There was a blast and then a flash of fire afterwards. There were bodies everywhere.”
Teenager Abigail Walker, who was at the concert, told the BBC: “I had to make sure I had my sister. I grabbed hold of her and pulled hard. Everyone was running and crying.
“It was absolutely terrifying.”
Charlotte Campbell’s daughter Olivia is among those who have been missing since the concert.
“She’s only a 15-year-old girl, she’s out there on her own because her friend has been found,” she told the BBC.
Analysis: Gordon Corera, BBC security correspondent
The UK threat level has been judged to be severe for nearly three years – which means an attack is considered highly likely.
But in recent months the tempo of counter terrorist activity has been increasing with – on average – an arrest every day.
After the attack in Westminster by Khalid Masood in March, police and security officials have been warning that further attacks were almost inevitable.
But they also believed that those were more likely to be low-tech involving knives or vehicles. The fact that the Manchester attack involved explosives will worry them.
It may not have been at the level of complexity seen in Paris in 2015, when multiple attackers sent from Syria used guns and suicide belts, but it will still have required planning.
The blast happened close to the entrance to Victoria railway and tram station. The station has been closed and all trains cancelled.
Greater Manchester Mayor Andy Burnham said the city would “pull together”, adding: “That’s what we are. That’s what we do. They won’t win.”
The Manchester Arena or MEN is the city’s largest indoor venue with a concert capacity of about 21,000.
Police are encouraging anyone with footage from the scene to upload it at ukpoliceimageappeal.co.uk or ukpoliceimageappeal.com. Other information can be reported to the anti-terrorist hotline on 0800 789 321.
IMAGES:
Theresa May says the Manchester attack was an act of ‘sickening cowardice’ BBC
GETTY IMAGES
Ian Hopkins from Greater Manchester Police gave an update on casualties BBC
MAP BBC
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Olivia Campbell, 15, has been missing since the concert FAMILY PHOTO
The wounded are being treated at eight hospitals around the city GOODMAN/LNP/REX/SHUTTERSTOCK
Manchester Arena incident: Eyewitness describes ‘explosion’ BBC
Mum Emma was 15 feet from blast at the Manchester Arena as she collected her children. BBC
Victim Georgina Callander was pictured with singer Ariana Grande two years ago BBC
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