The 35-year-old has dealt with right elbow soreness all spring. Crisp went 0-for-3 with a walk in a Minor League game Tuesday, and A's manager Bob Melvin said the outfielder was bothered by a few of his swings and was still sore Wednesday.
The A's are already without outfielder Josh Reddick, who will begin the year on the disabled list with a right oblique strain, though he could return in early April. Billy Burns is the likely candidate to take Crisp's place on the Opening Day roster.
Crisp is entering his sixth season with Oakland. He hit .246/.336/.363 in 126 games in 2014.
Chad Thornburg is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.