The birth was reportedly induced on Thursday but there was no word on whether the baby girl had been delivered as of Friday morning. Neil is expected back with the team for Game 3 of the Stanley Cup final on Saturday night.
"His wife's having a baby so I offered him a day off," coach Bryan Murray said. "I'm not sure how he'll be emotionally, but I'm sure it will be very good after it happens."
Patrick Eaves took Neil's spot on the third line with Antoine Vermette and Chris Kelly for practice.
Neil has been without a point in the 12 games since Ottawa's first-round series win over Pittsburgh. The top two lines were intact.
The Senators trail 2-0 in the best-of-seven series but hope home ice for Game 3 will help turn the series around.
"We know we didn't play our best and we still had a chance to win both games, so that makes us feel a lot better," said defenceman Chris Phillips.