The fight was scheduled to take place later in the day during a televised portion of a UFC Fight Night event in Natal, Brazil. The UFC has also terminated Chope's contract.
The promotion released a statement on the situation on Sunday morning.
"Tonight's featherweight bout between Will Chope and Diego Brandao has been canceled after UFC officials were made aware of Chope's previous military conviction," the statement read.
"The UFC does not condone behavior of this nature whatsoever and Chope has been released from his contract."
The UFC's decision comes one day after Bleacher Report first reported on Chope's background. A military judge convicted Chope, 23, of three specifications of assault consummated by a battery.
According to court documents, Chope threatened his wife with a knife and silenced her cries with a pillow or blanket during an argument about a joint credit card in November 2009.
Chope (19-6) made his UFC debut in January, losing to Max Holloway via TKO in the second round. He issued a statement on his release on Facebook.
"My fight has been canceled for a 5-year-old mistake I made," Chope wrote. "I am truly sorry to all the fans and will do everything I can to make this right.
"I have spoken with my ex-wife on the phone and she supports what I am doing and together we will make a formal press release as soon as I get back to the USA on Wednesday."
Brandao (18-9), who was scheduled for his first appearance of 2014, will be paid his show and win money, according to the UFC.