Pedroia's wife, Kelli, is due to deliver the couple's first child in August.
"She's about seven weeks away," said Red Sox manager Terry Francona after a 6-0 loss to the A's. "She had to go into the hospital today. He came back [briefly] after going over for the checkup. He didn't need to be at the ballpark today. He needed to be with her."
The Red Sox inserted Julio Lugo into Pedroia's No. 2 spot in the batting order. Lugo started at shortstop, while Nick Green moved to second base.
Pedroia, who was voted in as a starter to the American League All-Star team, went 3-for-5 in Sunday's win over the Mariners, adding a homer, a double and an RBI while scoring two runs.
For the season, Pedroia is hitting .290 with three homers and 36 RBIs.
Lugo, who has been used sparingly in recent weeks, is hitting .284 with one homer and eight RBIs. He went 0-for-4 on a night A's lefty Brett Anderson fired a two-hit shutout.
Francona wasn't sure if Pedroia will play Tuesday.
"We love when Pedey is around, obviously, but I wouldn't even come close to asking him," Francona said. "The only question I'll ask him is how is Kelly doing?"
Ian Browne is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.