Caffeine is frowned upon by the Mormon church, which owns BYU, but a delivery person accidentally loaded the machine up with the caffeinated version of the soda on Tuesday.
"Coke mistakenly included a limited number of caffeinated Coke Zeros in our order, which no one caught while the vending machines were being stocked," BYU spokeswoman Carri Jenkins said in an email to The Salt Lake Tribune.
The newspaper said the mistake was broadcast over Twitter by a Provo resident, who said there was a brief run on the machine.
The Tribune said caffeine is not directly banned by the Church of Jesus Christ of Latter Day Saints. The church does, however, bar coffee and hot tea, which has led to a school of thought that caffeinated sodas are also included.