For now, Oakland will stick with a mix of Sam Fuld and Craig Gentry in left field.
Crisp, who already missed the first month of the season while recovering from right elbow surgery, was limited to 126 games last year because of the same neck issue, including just 111 in the outfield.
When he was healthy enough to play in 2014, Crisp hit .246 with a .699 OPS.
"He had to make some adjustments at the plate as far as turning his head and maybe opening up a little more to try to get both eyes on the baseball," said A's manager Bob Melvin. "Whether he has to do that again, I'm not sure yet."
• Ben Zobrist will play seven innings in the outfield for Class A Advanced Stockton on Wednesday night, and he and left-hander Sean Doolittle will both join Triple-A Nashville in Fresno, Calif., on Friday.
• Right-hander A.J. Griffin (Tommy John surgery), who was scheduled to throw a bullpen session Wednesday, could pitch a two-inning simulated game on Tuesday and then potentially begin a rehab assignment shortly thereafter.
• Left-hander Eric O'Flaherty (left shoulder) is expected to throw a bullpen session by week's end.
Jane Lee is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.