Elbert, a lefty, is 2-0 with a 3.77 ERA in eight appearances with the Dodgers this season.
Torre said that Schmidt's situation was "not a surprise," considering all the past problems that have plagued him.
Torre, who spoke with Schmidt on Thursday, told reporters that Schmidt's next move will be to rehab his arm, and that he could possibly see the veteran contributing to the club in September.
"He had four starts," Torre said. "I think when it went along and he had start after start, we were all trying to find out things. It's unfortunate. I was happy he was able to get on the mound. I was happy he had especially the one good outing in Atlanta.
"I think he was finding things out with the rest of us."
Schmidt was up and down throughout his four starts with the Dodgers this season. He went 2-2 with a 5.60 ERA, couldn't last beyond the fourth inning in two of his starts and also threw six shutout innings against the Braves on July 31.
Tony Abreu was recalled from Triple-A Albuquerque to take Schmidt's place on the roster.
Abreu last played for the Dodgers in 2007, when he appeared in 59 games and hit .271 with two home runs and 17 RBIs.
Abreu missed part of the 2007 season and all of 2008 following hip and groin problems, and he was thought to be one of the Dodgers' best Minor League prospects.
Torre said that Abreu could play either second base, third or shortstop, but the manager didn't say exactly when Abreu would get playing time or how long he'd be in Los Angeles.
"Maybe for the weekend, maybe more than that," Torre said, "we're going to try to figure that out."
Abreu was batting .342 in 37 games with Albuquerque.
David Ely is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.