Manager Jayce Tingler said Hosmer could be out two to six weeks.
"Knowing Hos, he's a tough guy, and knowing his pain tolerance ... with some good luck and some good fortune, it heals up, and at that point, it'll be up to pain tolerance," Tingler said. "If we can get it to that point, I feel very confident betting on the man.''
The Padres have options at first base. Rookie Jake Cronenworth played well at first base when Hosmer missed several games early in the season because of a stomach ailment, and the Padres obtained Mitch Moreland during a flurry of trades in the days before last week's deadline.
"This one hurts,'' Tingler said. "But at the same time, we're going to have some guys step up. We're going to hold ground, and we're going to get him back. When he gets back, we're going to be in a good position.''
Hosmer was injured while bunting with two strikes for the second out of the first inning and was taken out of the game. He was replaced by Moreland.
Later in the contest, Hosmer was in the dugout with what appeared to be a splint on the injured finger.
Hosmer has been having a good season, hitting the ball in the air more than he had in recent seasons. He is hitting .291 with eight homers and 32 RBIs, and he was part of the Padres' "Slam Diego'' outburst in mid-August, when they became the first team in MLB history to hit four grand slams in four straight games.
San Diego hasn't been to the postseason since 2006.
The Associated Press contributed to this report.