Hundley's daughter weighed in at seven pounds, 12 ounces.
The Padres purchased the contract of catcher Chris Robinson from Triple-A Tucson to fill in while Hundley is on paternity leave. Robinson arrived just before batting practice in advance of Thursday's game against the Mets.
The 29-year-old Robinson, who has never appeared in a big league game, was hitting .298 in 29 games with Tucson with 12 RBIs. He was acquired from the Orioles for cash considerations on June 20.
"A veteran catcher, a good catch-and-throw guy, solid defensively, comes with a lot of experience, calls a good game," said Padres manager Bud Black. "Our scouts felt he was a guy you can trust your young Minor League pitchers with or a Triple-A staff with, and they had no problem with him catching in a Major League game if needed."
Black said he planned on talking to Hundley at some point Thursday evening, before or after the game.
Hundley is required to miss Thursday's game and is allowed to miss up to three games before returning.
Earlier Thursday, the Padres transferred pitcher Jason Marquis from the 15-day disabled list to the 60-day disabled list, creating an opening on the 40-man roster, which is at 39. Marquis had reconstructive elbow surgery earlier this month and will miss the rest of the season.