Holland leads the majors with 33 saves as Colorado entered Wednesday’s action in second place in the National League West and holding down the top wild-card spot.
Black said Holland was unavailable Tuesday night because of the injury.
“He cut his index finger on his throwing hand,” Black said. “It’s really day to day. We’ll see how it progresses the next five or six hours.
“He gave it a shot [Tuesday night]. He got up and threw but it wasn’t going to happen. This is one of those Mother Nature things.”
Holland was signed by Colorado in the offseason to a one-year, $7 million deal after missing all of 2016 because of Tommy John surgery.
He has had a huge bounce-back season, with a 1.64 ERA and 50 strikeouts in 38⅓ innings.
Holland spent his entire career with Kansas City, with 125 saves between 2013-15 before getting injured.