Oakland promoted Mazzaro, 22, to start the second game of a four-game series against the White Sox at U.S. Cellular Field.
Cameron had a save and a 3.44 ERA in 11 appearances with the A's after being promoted from Sacramento on April 29. He walked two, one of them forcing in a run, and gave up a hit in two-thirds of an inning Monday, his first outing since allowing a career-high-tying four earned runs on Saturday at Texas.
"He's going to help us in the future, for sure," Oakland manager Bob Geren said of Cameron before Tuesday's game. "Like all of our relievers, he's had some ups and downs, but I'm sure he'll be back at some point, and he's going to help us -- good guy, good pitcher."
Mazzaro essentially is taking the rotation spot previously held by righty Edgar Gonzalez, who was promoted from Sacramento on May 19 and went 0-1 with a 5.40 ERA in two starts, including a five-inning stint at Texas on Friday in which he gave up five earned runs on eight hits and three walks.
Gonzalez, 26, was moved to the bullpen Monday and will remain there as the designated long reliever.
"I like to have Edgar's innings out there," Geren said. "He can get out to 100 pitches; he's built up. With five young starters, you want to have ... someone who can step in and give you some length if one of the guys has a short outing."
Giese, placed on the 15-day disabled list on May 18 retroactive to May 16 with right elbow ulnaritis, was 0-3 with a 5.32 ERA in seven games, including one start. Originally eligible for activation May 31, he's now unavailable until mid-July.
Mychael Urban is a national writer for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.