Staff were evacuating fans when rain and winds of 70-80mph (113-128 kph) knocked over the concert entrance trusses, the venue said in a statement.
All of the people injured were taken to hospital. Two have since been released.
In a tweet, the US band cancelled the show, saying: "We never want to put our fans in harm's way."
The venue hosting the concert, WinStar World Casino and Resort, said in a statement that it had asked its patrons to seek shelter from the storm at about 1700 local time (2200 GMT) on Saturday after lightning was spotted within four miles of the site.
"However, about 150 patrons who were standing in line for the Backstreet Boys concert did not heed staff's warnings," it continued.
When the storm hit, it knocked over trusses and the entrance collapsed on top of them. The casualties were treated at the scene and transported to nearby hospitals.