Hill fouled a pitch off his ankle in Sunday's second game and was removed a few innings later.
After Gibson received the text, he talked with head athletic trainer Ken Crenshaw, and the decision was made to keep Hill out until Tuesday.
"All things considered, we're going to give him another day, and he's available [to pinch-hit]," Gibson said. "I'm sure he's going to hit in the cage. And he had a pretty big knot on there. And actually he could play the field OK, but the hitting really bothered him."
Hill entered in the seventh inning Monday as a pinch-hitter and flied out to center field.
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.