Manager Bruce Bochy said Ortmeier wasn't sure how he got injured, but the finger became swollen before Thursday's game at Arizona and he tried to play through it. X-rays on Friday revealed the fracture.
"He said he was fine to go but you could tell it was affecting him," Bochy said. "I'd say we're looking at four weeks."
The Giants called up outfielder Brian Horwitz, purchasing his contract from Triple-A Fresno. To clear room on the 40-man roster, San Francisco transferred injured left-hander Noah Lowry to the 60-day DL as he recovers from surgery on his throwing forearm.
Bochy said the Giants went with Horwitz over Nate Schierholtz because he provides a right-handed bat to be used in certain situations.
"We felt that was a need right now instead of Nate coming up here and being more of a role player," Bochy said.
Horwitz is on a major league roster for the first time in his career. The 25-year-old was batting .294 (40-for-136) with five home runs and 18 RBI in 44 games for Fresno this season. He played his college ball at nearby California across the bay in Berkeley.
He was in big league camp for part of spring training.
"I will just play day to day," Horwitz said. "I don't know what the future is going to bring. I'm happy to be here. It's all kind of surreal to me. Hanging with these guys and learning from these guys, I tried to take as much as I could out of spring training."
The 27-year-old Ortmeier began the season as the team's starting first baseman but that didn't work out as the club had hoped and he has primarily been playing in the outfield since April 15 in his rare starts. He was hitless over his last 17 at-bats spanning eight games and is batting .219 with no home runs and five RBIs this year.
Lowry, meanwhile, was shut down in late April after still feeling the tingling in his left forearm that forced him to undergo surgery to repair his nerves in March. But he could begin playing some light catch in the coming days, Bochy said. Lowry reported feeling "much better."
"He's a ways away," Bochy said.