The move is retroactive to May 13 and the A's called up right-hander Connor Robertson from Triple-A Sacramento to take his place on the roster.
Street, the 2005 AL rookie of the year, is scheduled to get a second opinion on his throwing arm from Angels orthopedist Dr. Lewis Yocum on Wednesday morning along with a second MRI exam. His initial test Monday showed no structural damage in the elbow.
He last pitched Saturday and had a 1-2-3 ninth with two strikeouts against Cleveland before feeling some discomfort Sunday when he tried to play catch.
"The nerve is acting up," Street said before the A's hosted the Kansas City Royals. "It happens. It's basically tendinitis in your arm. This is a first for me. I've never had anything lasting. As a pitcher, you have numbness and tingling and it goes away. This has been a week."
Street is 2-1 with a 2.50 ERA in 18 relief appearances this season, converting nine of his 11 save opportunities. He has allowed two runs over his last 13 outings and has held opponents scoreless in 15 of his 18 outings. The 23-year-old Street was also on the DL from Aug. 19 to Sept. 8 last year with a strained right groin and missed time in April with a strained muscle in his chest.
"Hopefully he'll just rest that and be fine," manager Bob Geren said.
Justin Duchscherer will assume the primary closer job, but several others could also be used in ninth-inning situations.
Geren also said Tuesday that right-hander Esteban Loaiza, on the DL recovering from a bulging disk in his neck, complained of soreness in his right knee during a throwing session Monday that could set him back in his schedule.
Robertson traveled Tuesday from Des Moines, Iowa, to the Bay Area via Salt Lake City. The 25-year-old has never pitched in the majors, and his parents in Alabama were working to make travel plans to Oakland to be on hand for when he makes his big-league debut.
He went 4-0 with two saves and a 1.93 ERA in 15 relief appearances for Sacramento. Geren plans to use him in a non-pressure situation at first if at all possible and "try to break him in the right way."
"I'm here to help out and do the best I can," Robertson said.
The A's have needed the disabled list nine times already this season, and Street became one of seven players currently on the DL -- making Geren's job as a first-year skipper that much more challenging.
"I've experienced a lot of turnover and change in the minor leagues when you have to mix and match," Geren said. "You adjust to it and do the best you can."