Arenado led off the second inning with a double to left field. His slide beat shortstop Andrelton Simmons' tag, a play that stood following a review that lasted 3 minutes, 48 seconds.
Rockies manager Walt Weiss said he doesn't know if Arenado will need surgery on the finger, but it's likely that he will require a trip to the disabled list. Shortly after the injury, infielder Josh Rutledge was recalled from Triple-A Colorado Springs.
"He'll miss some time," Weiss said. "It's tough news for our club. He's off to a great start and a hell of a player."
Arenado, who is hitting .305 with six home runs and 28 RBIs, is the latest in a long line of major leaguers to suffer a finger injury as the result of a head-first slide into a base. Already this season, the Tampa Bay Rays' Ben Zobrist, Washington Nationals' Bryce Harper and Los Angeles Angels' Josh Hamilton have sustained finger injuries from head-first slides into a base.
The loss of Arenado would be a blow to a Rockies lineup that was missing outfielder Carlos Gonzalez for the second straight game with a swollen left index finger.
The Associated Press contributed to this report.