Crawford was at the facility in the weight room, working on upper body conditioning, on Wednesday morning and received antibiotics.
"Since he was feeling a little ill, there's no reason to rush him back in right now," the training staff member said.
Crawford started a game on Monday in left field, struck out looking in his only at-bat in the first inning and came out when he told trainers he wasn't feeling well. He was taken back to the clubhouse on a cart. Crawford did not make the trip to Australia for the Opening Series against the D-backs because he is expected to go on paternity leave.
Among the other players left behind, outfielder Matt Kemp, recovering from offseason shoulder and ankle surgeries, had a scheduled day off from in-game activities, and right-hander Zack Greinke had a planned bullpen session. Righty Dan Haren threw a bullpen on Tuesday. Haren and Greinke remained in Arizona because they weren't scheduled to pitch in the two-game series to be played on Saturday.
The veteran Crawford missed workouts and action last month because of right quad and hamstring tightness, but he has played regularly. He spent a month on the disabled list last year with a strained left hamstring.
Barry M. Bloom is a national reporter for MLB.com and writes an MLBlog, Boomskie on Baseball. Follow @boomskie on Twitter. This story was not subject to the approval of Major League Baseball or its clubs.