Harrison jammed his thumb Sunday while stealing a base in the seventh inning of a win over the Cleveland Indians. He is scheduled to undergo testing to see if there is any structural damage and also to determine a timetable for his return.
In 75 games, Harrison is hitting .279 with four home runs and nine stolen bases. He was second in the NL last season with a .315 batting average in his first year as a regular.
"We play with dings and bruises all the time," Harrison said. "That's part of the game. That's baseball. You can't get upset about it.
"We have a great training staff and we'll get with those guys and get back in the lineup as soon as possible."
Right fielder Gregory Polanco, who is hitting .231, was scheduled to bat leadoff on Monday. Manager Clint Hurdle said he might try some different players in that spot.
Also, left fielder Starling Marte was not in the lineup after leaving Sunday's game with discomfort in his left side during a fourth-inning plate appearance.