The Angels hitmaker was performing at the city's Metro Radio Arena on 22 June, when he fell off stage while trying to high-five fans and landed on Margaret Nash's arm, according to The Mirror newspaper.
The 52-year-old was treated by medics at the venue before she was taken to a nearby hospital, where it was discovered she had broken her arm.
The venue's general manager Paul Tattenden says that he was made aware of the incident and Williams' team have been in touch with the injured fan.
He said: “We attended to the lady after she said she had pain in her arm.
"We were later told she had broken it. We got in touch with Robbie’s production company and they have been in touch with the lady."