Hill initially stayed in the game, playing defense in the bottom of the sixth, but Didi Gregorius pinch-hit for him in the seventh.
"He could throw, but he couldn't hit," D-backs manager Kirk Gibson said. "We'll see how he feels tomorrow. I don't have him in the lineup right now."
Hill was hit in the left hand by a pitch last April, and though X-rays showed no break, an MRI later showed a non-displaced fracture. He missed more than two months recovering.
"I don't think it hit him as solid," Gibson said, comparing this year to last. "We'll see how it is tomorrow."
Hill had been the subject of trade rumors of late, and with less than a week to go before Thursday's non-waiver Trade Deadline, any missed time could hurt his value.
Steve Gilbert is a reporter for MLB.com. Read his blog, Inside the D-backs, and follow him on Twitter @SteveGilbertMLB. This story was not subject to the approval of Major League Baseball or its clubs.