Cabrera, who flew from Philadelphia to San Diego on Monday, was diagnosed with the fracture by team physician, Dr. Jan Fronek. The injury to Cabrera's hand occurred in the sixth inning when he fouled a pitch off.
Black made it clear Monday that Cabrera will be able to resume playing in games in six to eight weeks and he wouldn't need the two full months to recover before he could begin participating in baseball-related activities.
"This is an injury and surgery guys come back [quickly] from," Black said.
San Diego general manager Kevin Towers, who has been on this road trip, said the he is working the phones to get the team a player to help their middle-infield depth.
"We hope to have someone in place by San Francisco. We would prefer to get a starter but we're in a bind, we have to do something quickly. More than likely, that person will be from outside the organization," Towers said.
The Padres are believed to be looking into trading for veteran shortstop Chris Burke, who spent nearly all of Spring Training with the team before being told on March 25 that he wasn't going to make the 25-man Opening Day roster.
Burke was then traded later that day to the Mariners for cash considerations and has been playing with their Triple-A team in Tacoma, where he was hitting .238 with one home run and three RBIs in 38 at-bats.
Burke hit .281 with a double and three RBIs in 32 at-bats in Spring Training, playing third base, second base and shortstop for the Padres.
The Padres currently have Edgar Gonzalez on their roster as their lone infield reserve.
The 22-year-old Cabrera, a Rule 5 Draft selection in December, was hitting .308 in six games, four of which were starts behind Luis Rodriguez. He had two hits in Sunday's game and injured himself in his third at-bat.
"The kid had made great strides from the middle of February until now. You could see the confidence grow," Black said. "He improved on the nuances of the position. He was becoming more and more comfortable with his environment.
"He'll be back in less than two months. He'll be ready to go."