Authorities believe they know the identity of the assailant, she added, "but at this stage of their investigations, we can not confirm his name".
Greater Manchester Police said they were called to the venue at around 10.33pm and approach roads were closed.
A video claiming to be from an Islamic State soldier took responsibility for the attack and claimed "this is only the beginning".
As the crowd began to move, many of them children wearing bunny ears like their idol, eyewitnesses at Monday's concert at the Manchester Arena described a loud, sharp bang, and then chaos broke out. Police have determined the attack was carried out by a lone male suicide bomber, who detonated an improvised explosive device and died in the blast. Trump's message of condemnation, mixed with the pragmatic acceptance that we have not seen the end of this problem, marked a moment of maturity for a man often given to wild exaggeration and over-promising.
Africa stands with the people and government of the United Kingdom in reaffirming our solidarity with them during this hard time.
After Manchester, Grande was due to perform in London on Thursday and Friday, and later at venues in Europe, including Belgium, Poland, Germany, Switzerland and France, with concerts in Latin America and Asia to follow.
Seconds after the blast, Niamh Woods told her father people were "frantically banging" on the door to try and get away from the scene of the explosion.
Scots are among those being reported missing, with anxious parents taking to social media to appeal for information.
Hollie Simpson and her daughter Maddison left at the interval and heard about the attack while eating in a nearby restaurant. She was killed last night Manchester.
"It came as a total shock and I can't even put into words how it feels when something like this happens so close to the place I've called home for almost two years".
Greater Manchester Mayor Andy Burnham described the attack as "our darkest of nights".
It is the worst terrorist strike on British soil since 2005, when Islamist extremists bombed the London subway and a bus, killing 54 people.
Hotels across the city took frightened music lovers who attended the event under their wing last night.
But especially in more sparsely populated areas, police unions have argued that training efforts are proceeding too slowly and that the few armed officers available would likely arrive at the scene of an attack too late.
May said Britain's terror threat level had been raised to critical - meaning another attack may be imminent.
Grande, who is wildly popular both in Britain and the United States, was not injured in the attack.
Concertgoers are starting to accuse security at Manchester Arena for not being strict enough prior to the suicide bombing Monday night at an Ariana Grande concert.
"The concert had finished and we were all leaving and there was an explosion to our left and people started running", television actress Isabel Hodgins, who was at the show, told Sky.
"The South African government condemns in the strongest terms terrorist attacks in any form and from whichever quarter and in particular, against innocent children and youth", said the Department of International Relations and Cooperation.
The local ambulance service said 59 people were taken to hospitals.
Fans of Grande had come from across northern England to see the concert.
Public transport shut down, and taxis offered to give stranded people free rides home, while residents opened their homes to provide lodging.
"It brings out the people's good spirit", White said, referring to the sense of solidarity that could be felt throughout the city in the wake of the attack. "There was this heat on my neck and when I looked up there were bodies everywhere".