X-rays taken on Holliday were negative, and manager Mike Matheny said the slugger is day-to-day.
Holliday, the third batter in Wednesday's game, was hit on the left elbow by a 94 mph fastball. He backed away from the plate after being hit, removed his helmet and fell to one knee in pain.
Matheny and a trainer checked on Holliday, who slowly walked to first base.
Holliday remained in the game temporarily but was replaced in left field by Pete Kozma in the second inning.
Kluber set down 18 straight batters after hitting Holliday. He struck out 18 and allowed his only hit in the seventh inning in leading the Indians to a 2-0 win. He was pulled before the ninth with 113 pitches.
Cardinals pitcher John Lackey hit Jason Kipnis in the back in the fourth inning. Plate umpire Mike Everitt issued warnings to both teams, which led to the ejection of Indians manager Terry Francona, who vehemently argued with Everitt and crew chief Tim Welke.
Kipnis was hit again in the sixth by reliever Randy Choate to load the bases. Kipnis singled in the eighth and made sure the Cardinals saw him flip his bat as he headed toward first.
The Associated Press contributed to this report.