Shula Coward was in the foyer after the Ariana Grande concert when Salman Abedi detonated the bomb which killed 22 people on 22 May.
She said she instinctively grabbed her 11-year-old daughter Acacia and her friend and they ran.
"There was a bang, then firecracker noises, lights flashing and smoke... and it went very quiet," she added.
Ms Coward said her daughter's friend was crying so she took her hand and they ran for the exit.
She told BBC Radio Manchester: "We stopped for a spilt second when it was quiet. I remember looking up at the ceiling and you could see like all black pieces coming down.
"I realised straight away. I saw my daughter being lifted up the air and land on the floor.
"I reached forward and dragged her up off the floor. I didn't even look to see if she was injured.
"As we reached the exit door I could see my daughter was slowing up and she said 'I can't run anymore, my leg is really hurting'.
"I realised then she had been injured."
Ms Coward said it was like being in a "war zone" with people being stretchered out and others frantically searching for their loved ones.
The bolt from the bomb imbedded in her daughter Acacia's knee but the force of the blast pushed it two inches down into her leg, damaging an artery.
Acacia is now recovering at home and the netball fan was cheered up by a surprise visit from some of the members of her favourite team Manchester Thunder.
A woman who was caught up in the Manchester Arena attack says she felt like she was in a "war zone".