Byrnes had a screw and plate placed in his fifth left metacarpal in an operation performed by Phoenix hand specialist Dr. Don Sheridan.
Diamondbacks manager A.J. Hinch said Byrnes is expected to miss between 4-8 weeks.
Byrnes is the 10th player Arizona has put on the disabled list this season.
Also on Friday, the Diamondbacks purchased the contract of outfielder Alex Romero from Triple-A Reno to take Byrnes' spot on the active roster. They transferred right-hander Tom Gordon to the 60-day disabled list to make room on the 40-man roster.