Harper had said he hoped to play in at least one of the three games against the San Diego Padres. But he still experienced soreness from Sunday's injection and was not in the lineup against the Padres.
Manager Joe Girardi said he would "keep our fingers crossed" that Harper could play Friday against the Dodgers.
The reigning National League MVP, Harper had the injection Sunday because of a small tear in the ulnar collateral ligament of his throwing elbow that has forced him into the role of designated hitter. He hasn't played right field since April 16 and will remain as the DH whenever he returns. He is unable to throw for at least six weeks.
The 29-year-old Harper is batting .305 with nine home runs, 14 doubles, 27 RBIs and a .634 slugging percentage.