Proceeds from the show will benefit the "We Love Manchester Emergency Fund", in partnership with the British Red Cross and Manchester City Council.
Police named Abedi, 22, as the suicide bomber behind the May 22 attack at the Manchester Arena.
"Ariana brought everyone a sunflower and a teddy bear", Lauren Thorpe, the mother of 8-year-old Lily, told CNN.
Shortly after her visit, Ariana took to social media to share a touching picture of herself with a young fan.More news: Newest Statue on Wall Street: 'Pissing Pug'
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Peter Mann, whose daughter Jaden was hurt, posted images of the visit on Facebook. He posted photos of Grande and Jaden on Facebook and wrote: "This means more to us than all the wonderful things people have done this week".
"So happy she came i could burst!", he wrote. "Even cried again myself".
Mr Adam Harrison told the BBC his daughter Lily "felt like a rock star" after meeting her idol late on Friday and was "chomping at the bit" to attend the concert.
For more on Grande's One Love Manchester concert, watch below.
Police said 17 people have been arrested in connection with the investigation.
A bomb-disposal team was called out and the auto was removed.
The festival was evacuated on Friday evening after Koblenz police said they were in possession of "concrete elements, in the light of which a possible terrorist threat can not be ruled out".