Manager Kirk Gibson made the announcement after the team's 6-2 loss to the Cleveland Indians on Wednesday.
Mora struck out in a pinch-hit appearance. The 39-year-old third baseman is batting .228 in 127 at-bats. He figured to be the starter when he was signed as a free agent in the offseason, but injured his neck in a car accident during spring training. The job eventually went to Ryan Roberts.
Mora has played in the majors for parts of 12 seasons, mostly with Baltimore.
Gibson said the corresponding move would be made on Friday, when the Diamondbacks open a three-game series at Oakland.