Randy Snell says Kid Rock lit the cigar while attending country singer Travis Tritt's show Friday at Andiamo Celebrity Showroom in Warren.
Spokesman Nick Stern told The Detroit News that Kid Rock offered his "most sincere apologies" to patrons he may have offended. He said he had been drinking alcohol.
Randy Snell, 58, of Trenton, has asthma and says he plans to file a health department complaint. Michigan law prohibits smoking at workplaces including bars and restaurants.
Kid Rock was born Robert Ritchie. He grew up in and lives in suburban Detroit.