The 90s boyband was set to perform at a resort in Thackerville when a storm struck and trusses holding up an entrance collapsed.
Band member Kevin Richardson tweeted earlier that the concert had sold out, with about 12,000 fans expected to hear the group.
WinStar World Casino and Resort said that an evacuation began at about 5pm, when lightning was within four miles of the casino.
But 150 people did not evacuate when the storm hit, bringing winds of up to 80mph, the company said.
Many of them were hit by the collapsing entrance.
All of the 14 injured were taken to hospital and two have since been released.
Richardson later said: “Severe weather, high winds and rain just passed thru here in Thackerville, OK.
“Emergency crews are on the seen as tent (collapsed) and some folks who were seeking shelter were injured. Waiting to determine damage to our stage and production.”
The concert was postponed, with the band saying on Twitter: “We never want to put our fans in harm’s way and with tonight’s weather and the injuries from earlier, we have decided to cancel the show and will attempt to reschedule.
“The most important thing is for everyone to get home safely and we will see you all very soon!”