Players can take up to three days of paternity leave.
"He had a reason to go today," Phillies manager Ryne Sandberg said.
The Phillies played Wednesday's series finale against the Rangers at Globe Life Park with 24 players. If and when they place Rollins on paternity leave, they would be allowed to replace him on the roster.
"When the baby is delivered, we'll go from there," Sandberg said.
Jayson Nix is expected to play shortstop while Rollins is out. Cesar Hernandez would only be played there in an emergency situation.
"He's very steady, very professional, very polished infielder," Sandberg said of Nix. "I heard good things about his glove, and after watching him take ground balls, he's fundamentally sound. I've also been impressed with his batting practice, and his at-bats last night."
Todd Zolecki is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.