The team has not set a date for Pedroia's return.
"I told him his first responsibility is Kelli and that child," Red Sox manager Terry Francona said, adding that the second baseman got on a 1 p.m. ET flight to Boston and went straight to the hospital upon his arrival.
"We don't know when he's going to come back, and he can take his time, because having your first child, that's a great thing in life, and we're excited for him," Youkilis said.
Pedroia arrived in time to witness the birth of seven-pound baby Dylan, and the family is doing well, according to a team official.
Pedroia, the American League's Most Valuable Player in 2008, was voted the starting second baseman for this year's All-Star Game, but missed the event when Kelli went into labor early and was hospitalized.
"I think it's a great thing after all she's been through and Dustin's been through, mentally," Youkilis said. "I think it's going to be a great thing for Dustin. We always joke about dad strength, so hopefully he comes back and keeps hitting home runs. It'll be a great thing for him."
Pedroia is batting .295 with 10 home runs and 51 RBIs this season. Nick Green, who has played shortstop most of the year, took over at second base in Tuesday's game.
While Pedroia was spending time with his new son, Youkilis, who has split time between first and third base this year, wasted no time getting back into action, smacking a pitch from Jays starter Ricky Romero into center field for a double in the second inning.
The Red Sox went 2-3 during Youkilis' suspension, which came as a result of his actions in Wednesday's tilt against Detroit. He charged the mound after being hit in the back with a pitch from the Tigers' Rick Porcello, who was also suspended for five games.
"You're playing in a game and you have shortness of breath after getting hit in the ribs -- I still feel it to this day. I don't think you can put on paper what that feels like," he said. "I have a family and this is my job, and at some point it's got to end.
"There's nothing that a hitter can do. It's not like we can try to hit that fastball or slider right off the guy's ribs. We can't do that. Pitchers have the power to throw at people, and it's one of those things that's been going on in baseball for years.
"The only thing I regret doing is, I have a charity, I have family. ... The only thing is it stunk that I hurt my team and not being able to play for my team, but it's one of those things where you've got to do it."
Youkilis, who was hitting .311 with 20 home runs and 66 RBIs through Monday, seemed eager to put the incident behind him.
"You can't take back what you do in life, and you just move on," he said. "I think we're just talking about this way too much in life. It's time to move on."