The Indie rockers, who hail from South Yorkshire, performed to a sell-out crowd at Network – formerly Plug – on Matilda Street on Saturday night.
But when the band were into their opening number, the barriers separating the crowd from the stage gave way and a number of fans were reportedly injured.
Yorkshire Ambulance Service confirmed that an ambulance transported one casualty to hospital.
The band temporarily halted the gig while checks were made on fans and until the crowd barriers were erected again.
A photograph has been shared on social media of one Reytons fan in hospital after the barrier collapse.
He wrote: “End of the day the barriers were not safe. Before the start they were very wobbly and did not look safe at all.”
Posting on The Reytons’ official Facebook page Matt Curran, who was at the gig, said: “I think it’s fair to say after last night that you’ve outgrown venues of that size especially in South Yorkshire.
“Glad you stopped when the barrier collapsed, perfect example to other acts and well done to the venue I have to say for ensuring everyone was safe before continuing. People were on the floor in front of us and was nice to see everyone pick each other up.”
Claire Mylett said her son and friend were injured and taken to hospital.
“Thank you to those that helped them,” she added.