Fellow band members apologized to fans via Twitter.
"Dallas, I cannot begin to tell you how sorry I am. There are internal sicknesses & problems that have needed to be addressed. No words," Jared Followill tweeted.
Drummer Nathan Followill called the incident a "fiasco."
"Not so good morning 4 me today," Nathan Followill tweeted. "Ashamed & embarrassed by last night's fiasco. Can't apologize enough, utterly gutted. A million I'm sorry's."
The band, known for hits including the Grammy Award-winning anthem "Use Somebody," plans to return to Dallas on Sept. 21 and to Houston on Sept. 22.