Right-hander Sean Gallagher will instead get the start Saturday against the visiting Blue Jays.
Anderson's blister, near the top of his left index finger, developed last week in Texas and forced him to walk off the mound in the bottom of the sixth inning. His next start was pushed back a day to give him more time to heal, but it wasn't nearly enough.
The blister again broke open in the first inning on Monday against the visiting Angels, and by the bottom of the fifth he couldn't go any further; Anderson gave up five runs on nine hits and a walk over 4 2/3 innings before again being ushered off the mound by a team trainer.
On Monday, Anderson was hopeful that he'd recover quickly because "all the bad skin" had torn off during the game, leaving behind what he called "baby skin."
Baby skin, of course, is awfully tender. Probably not something you want to test right away against the friction caused by the spinning seams of a baseball thrown at high velocity.
Anderson said the blister bothered him most while throwing fastballs, and fastballs are his meal ticket.
"It's what I use to get ahead [in the count] and what I use to put guys away," he said. "It's kinda tough when I can't go to that pitch when I need it."
Geren told reporters that placing Anderson on the disabled list "wouldn't be a consideration" for now.
"We've got two off-days next week, so that definitely helps," Geren said. "He'll basically have 10 days off; that's the plan for now."
Teams can put players on the DL retroactively up to five days after the day after the injured player's most recent appearance in a game, though, and if Anderson's blister isn't showing significant improvement by Friday, the plan could change.
If it does, Gallagher likely would get another opportunity to start as long as he pitches as well Saturday as he did upon taking over for Anderson on Monday. He worked 3 2/3 scoreless innings, giving up three hits without a walk while striking out three.
"He came right in and pitched exceptionally well," Geren said of Gallagher, who didn't win a spot in the starting staff during Spring Training despite entering camp as a near lock. "It's a perfect fit."
Gallagher opened the year in the A's bullpen and made three appearances before being optioned to Triple-A Sacramento to join the River Cats' rotation. He made two starts in the Minors and didn't allow a hit or a run over five innings while walking three and striking out seven.
Obtained in the trade that sent Rich Harden and Chad Gaudin to the Cubs last summer, Gallagher made two starts against Toronto last season. He lost both, allowing seven earned runs in a total of eight innings.
Mychael Urban is a national writer for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.