Holland leads the majors with 33 saves for Colorado, which currently holds the second wild-card spot in the National League.
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.