Davis has a 6.82 ERA this season, including an 11.29 ERA at Coors Field.
In his last appearance, Wednesday against the Dodgers, he allowed five runs in one-third of an inning, taking the loss to drop to 1-5 this season.
Davis signed a three-year, $52 million deal with Colorado prior to the 2018 season. He saved a National League-best 43 games last season but has struggled with his control so far this year, posting a strikeout-to-walk rate less than double (8.8%) that of last year's (19.9%).
Black said Scott Oberg (5-1, 1.59 ERA) will take over as Colorado's closer for the time being.