Martin Prado started at second base in the series opener at Yankee Stadium.
Hill was hit in the hand by a pitch from Pittsburgh's James McDonald a week ago. He made his first start since the injury on Sunday, and left in the fourth inning with soreness.
Hill is batting .306 with two home runs and six RBIs.
Gregorius made his major league debut last year with Cincinnati and was acquired in an offseason trade. He's been slowed by a sore elbow this year.