The attack sparked a nightlong search for loved ones - parents for the children they had accompanied or agreed to pick up, and friends for each other after groups were scattered by the blast.
Twitter and Facebook were filled with appeals for the missing.
There was no immediate claim of responsbility, but Chief Constable Ian Hopkins said police are treating the blast as an act of terrorism "until we know otherwise."
A police helicopter hummed over the city as somber commuters hurried to work.
Public transport shut down, and taxis offered to give stranded people free rides home, while residents opened their homes to provide lodging.
The concert was attended by thousands of young music fans in northern England. Grande, who was not injured, tweeted hours later: "broken. from the bottom of my heart, i am so so sorry. i don't have words."
Forensic investigations are trying to determine if the attacker had accomplices, Hopkins said. He provided no information about the person who set off the bomb.
He said some of the dead were children but provided no further details.
Hayley Lunt was staying at a hotel nearby and had taken her 10-year-old daughter Abigail to her first concert at Manchester Arena today.
She said the explosions rang out as soon as Grande left the stage.
"It was almost like they waited for her to go."
"We just ran as fast as we could to get away from that area," Lunt said.
"What should have been a superb evening is now just horrible."Campaigning for Britain's June 8 election was suspended.
The explosion struck near the exit around 10:30 pm Monday as Grande was ending the concert, part of her Dangerous Woman Tour.
Police cars, bomb-disposal units and 60 ambulances raced to the scene as the scale of the carnage became clear.
More than 400 officers were deployed.
"A huge bomb-like bang went off that hugely panicked everyone and we were all trying to flee the arena," said 22-year-old concertgoer Majid Khan.
"It was one bang and essentially everyone from the other side of the arena where the bang was heard from suddenly came running towards us as they were trying to exit."
Home Secretary Amber Rudd decried "a barbaric attack, deliberately targeting some of the most vulnerable in our society - young people and children out at a pop concert."
The local ambulance service said 59 people were taken to hospitals.
The city's regional government and its mayor, Andy Burnham, were among scores of Twitter users who circulated the MissinginManchester hashtag, used by people looking for family members and friends.
Among the names being circulated was Olivia Campbell. Her mother, Charlotte Campbell, said the 15-year-old attended the concert with her best friend from school.
He is hospitalized but Olivia is missing, the mother told ITV television's Good Morning Britain breakfast show.
"I've called the hospitals. I've called all the places, the hotels where people said that children have been taken and I've called the police.
"She said she last heard from her daughter just before the concert.
"If anyone sees Olivia, lend her your phone, she knows my number.
"There was no immediate claim of responsibility. Supporters of the extremist Islamic State group, which holds territory in Iraq's Mosul and around its de facto capital in the Syrian city of Raqqa, celebrated the blast online.
US President Donald Trump, in Bethlehem, said the attack preyed upon children and described those responsible as "evil losers."
"This wicked ideology must be obliterated. And I mean completely obliterated," he added.
If the explosion is confirmed as a terrorist attack it would be the deadliest in Britain since four suicide bombers killed 52 London commuters on three subway trains and a bus in July 2005.
Video from inside the arena showed people screaming as they made their way out amid a sea of pink balloons.
British Prime Minister Theresa May is due to chair a meeting of the government's COBRA emergency committee later Tuesday.
The Dangerous Woman tour is the third concert tour by 23-year-old Grande and supports her third studio album, "Dangerous Woman."
Grande's role as Cat Valentine on Nickelodeon's high school sitcom "Victorious" propelled her to teen idol status, starting in 2010.
After Manchester, Grande was to perform at venues in Europe, including Belgium, Poland, Germany, Switzerland and France, with concerts in Latin America and Asia to follow.Pop concerts and nightclubs have been a terrorism target before. Most of the 89 dead in the November 2015 attacks in Paris were at the Bataclan concert hall, which gunman struck during a performance by Eagles of Death Metal.
In Turkey, 39 people died when a gunman attacked New Year's revelers at the Reina nightclub in Istanbul.
Manchester, 260 kilometers northwest of London, was hit by a huge Irish Republican Army bomb in 1996 that leveled a swath of the city center. More than 200 people were injured, though no one was killed.
