Videos posted on social media showed thousands youngsters fleeing from the arena, situated in the north of Manchester city centre.
Grande had just finished her sold-out gig, releasing giant pink balloons from the ceiling as part of the finale, when the bomb went off.
"We heard a loud explosion and we weren't sure what it was at first. People were saying it was a balloon popping or a speaker had just overriding and busting," Sebastian Diaz, a 19-year-old at the concert, told AFP.
"People started to push their way forward and we realised something wasn't right. People around us were just screaming, crying.
"There were fathers carrying their little girls who were in tears. People were pushing down the stairs. It was just, it was chaos."
"People were injured by being trampled as they tried to get out. It was absolute carnage," Ryan Morrison, 19, told the Manchester Evening News.
"They were losing shoes, they were dropping phones," Stephanie Hill told AFP, her teenage daughter Kennedy adding: "One girl fell over the seats."
Stephanie added: "We ran, we picked up a young girl on our way who was hyperventilating saying she had lost her mum.
"We took her with us, tried to calm her down. We did find her mum."
Heartbroken mother Charlotte Campbell said she had not yet been able to find her daughter.
"I can't get through to her. I've called the hospitals, I've called all the places, the hotels where people say that children have been taken," she told television programme Good Morning Britain.
"I've called the police. There's no news, I've just got to wait. I'm waiting at home just in case she turns up here."
Videos posted on social media showed thousands youngsters fleeing from the arena, situated in the north of Manchester city centre, in a state of panic and confusion as sirens rang out from emergency services.
Andy Holey was hit by the impact of the blast when he arrived to collect his wife and daughter.
"An explosion went off and it threw me about 30 foot from one set of doors to the other set of doors," he told the BBC.
"When I got up I saw bodies lying on the ground. My first thought was to go into the arena to try to find my family. I managed to find them eventually and they're OK.
"It was definitely an explosion and it was some force. It happened near the box office at the entrance to the arena."
Elena Semino, was waiting for her 17-year-old daughter by the arena's ticket office when the explosion occurred, injuring her.
"There was heat on my neck and when I looked up there were bodies everywhere," she told The Guardian newspaper.
Cheryl McDonald, who went with her nine-year-old daughter, told Sky News television: "I've never been so scared in my life. My daughter is very, very shocked."
McDonald broke down as she described a "devastating" scene, saying the venue was "full of children".
Gary Walker, who had been waiting for his daughters, was hit by shrapnel in his leg, while his wife was hurt in the stomach.
"Someone came through the doors then bang," he told BBC radio.
His daughter Abigail said: "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."
Emma Johnson and her husband were at the arena to pick up their 17-year-old son and 15-year-old daughter.
"We were stood at the top of the stairs and the glass exploded. It was near to where they were selling the merchandise. The whole building shook," she told the BBC.
"There was a blast and then a flash of fire afterwards. We obviously then run to try and find our children and fortunately for us we were all safe to tell the story."