Manager Joe Maddon said on the team's Web site that the speedster is "a ways away" from swinging a bat and needs more time to fully heal from his Aug. 14 surgery.
The surgery was to fix a subluxation of his right middle finger tendon, a joint connecting the finger to the hand.
The tendon used to straighten the finger came out of its groove, which caused the finger to lock into position when he bent it downward.
Crawford was hurt while swinging at a pitch from J.J. Putz in the 10th inning of the Rays' Aug. 9 contest in Seattle.
"If they do make it to the World Series or the second round (of the postseason playoffs), I have a chance to come back," Crawford said.
Crawford has a .273 batting average with eight homers and 57 RBI.