The right-hander posted on his Twitter account late Wednesday night that he and his wife lost their first child 23 hours after his birth "with no explanation." He asked for prayers, and words of support began flooding Twitter.
Neshek took a flight home to Florida to be at the birth of Gehrig John Neshek on Tuesday.
"Our hearts go out to Pat and Stephanee and we share in their sorrow of losing their young son," the A's said. "The entire A's organization will keep the Neshek family in our prayers and thoughts, as they try to come to grips with this tragic occurrence in their lives."
Earlier in the day, the A's swept the Texas Rangers to capture an improbable AL West title. Neshek had been away from the club for the final two games.
The 32-year-old Neshek, acquired from the Baltimore Orioles in early August for cash considerations, was 2-1 for the A's with a 1.37 ERA in 24 appearances and 19 2/3 innings.