The illustrator said Elba, who was performing at Upper Campfield Market Hall in Manchester on Wednesday, stayed with her until paramedics were able to help and escorted her to an ambulance.
She told the Mirror: “I would love to thank him personally, but doubt I will cross paths with him, he’s very famous.”
Ms Billington, from Salford, was taken hospital and released after a check-up, the newspaper reported.
Tree was co-created by the Elba and Kwame Kwei-Armah and is being shown at Manchester’s international festival until July 13.