In a weekend series at Arizona Saturday, Bay was hit by a pitch from Elmer Dessens in the second inning. X-rays taken at Bank One Ballpark revealed the injury to be a fracture to the ulnar styloid bone, which is on the outside edge of the wrist.
Padres trainer Todd Hutcheson described the break as fairly clean with no other complications.
After getting plunked, Bay took his base and played the bottom half of the inning in the outfield, but was unable to answer the call for defensive duties in the third and was replaced by the recently-signed Gary Matthews Jr.
"I ran the bases and then I went out to the outfield and played catch and it didn't really feel all that great," Bay said. "It just started getting tighter as the inning went on, and thank God a ball didn't get hit my way. I went in and after that it just sort of locked up. I've never had a broken bone before, but I knew there was something wrong."
MLB.com, the Web site of Major League Baseball, reported that the injury normally requires a minimum of six weeks to heal, but in this case, that process may be quicker.
"It depends," Hutcheson said. "Doc (Jan) Fronek said 4-6 (weeks), but we'll have to reevaluate it as we go. Obviously, he'll be in a splint for a couple of weeks. We'll re-X-ray it to make sure the fracture hasn't moved positions. It's a non-displaced fracture so there is nothing else we have to do. Just immobilize it and let it heal."
Bay, 24, who in his major league debut on Friday homered off Arizona's hard-throwing closer, Matt Mantei, has been placed on the 15-day disabled list, where he joins the man he replaced, centerfielder Mark Kotsay, as well as closer Trevor Hoffman and left fielder Phil Nevin.
To fill his roster spot, the Padres have recalled Jermaine Clark from Triple-A Portland of the Pacific Coast League.
Clark, who was claimed off waivers on April 30, began the season with the Texas Rangers, but was demoted to Triple-A Oklahoma after batting just .188 in 10 games with the Rangers.
The Padres ended a dreadful 1-6 road trip Monday with an 8-4 loss to the Diamondbacks, and are last in the National League West at 14-37 overall, 7-21 away from home.