Gore was injured during a non-contact ball-handling drill, and coach Mike Nolan said he would not practice with the team for the remainder of the week. Gore will be re-evaluated next Monday, and Nolan expects him to return to practice then with a cast on his hand.
"He'll be ready for the latter part of preseason, but his participating in the preseason, we'll wait and see on that," Nolan said.
Gore set a franchise single-season record last season while leading the NFC with 1,695 yards rushing. He was the NFC's starting running back in the Pro Bowl after just his second NFL season.
One of the league's top young backs, Gore said he is aiming for a 2,000-yard season this year and hopes to challenge Eric Dickerson's NFL record of 2,105 yards that has stood for 22 seasons.
Gore has a considerable history of serious injury. He tore ligaments in each of his knees and had major surgery on both during his college career at Miami. After his first season with the 49ers in 2005, when he became the first rookie in 15 years to lead the team in rushing, Gore had surgery to repair a torn labrum in each of his shoulders.
That didn't prevent Gore from having a breakout season last year, when he also recorded a franchise-record 312 carries. He also led San Francisco last year with 61 receptions while setting a franchise record of 2,180 yards from scrimmage.
"I always like to see a silver lining in whatever happens," Nolan said. "This is going to give Michael Robinson, Hicks and the rookie an opportunity to get more reps and see what they can do."
Nolan said there's a possibility the 49ers will bring in another running back to provide depth in training camp until Gore returns. Robinson, Hicks and Clayton are the only other running backs on the team's summer roster.