The country star and his fellow bandmates were slated to play at the OKC Downtown Airpark venue in Oklahoma City, but will not be taking the stage as scheduled.
A statement on the band's official website attributes the axed gig to "an illness affecting Gary's vocals".
Ticketholders have been offered refunds for the scrapped show.
Rascal Flatts, who have been on their U.S. tour with opening acts Sheryl Crow and Gloriana, are still scheduled to play three dates in Texas this weekend (11-13Jul14).
It's not the first time Levox has struggled with vocal problems - he lost his voice days before the group's big gig at the Academy of Country Music Awards in April (14), but decided to press ahead with the show by miming along to the lyrics of Rewind. However, he was caught out by eagle-eyed fans and subsequently had to confess he had been lip-syncing.