Crawford hasn't played yet for the Red Sox this season, thanks to left wrist and elbow woes. He went 3-for-14 with five walks in five Gulf Coast League games in Fort Myers, Fla.
Jacoby Ellsbury played his third game in the Gulf Coast on Monday and drilled a home run, as well as walking and grounding out. Ellsbury played six innings in center field.
He will serve as the designated hitter on Tuesday in Florida and could join Crawford at Double-A as early as Wednesday.
Outfielder Ryan Sweeney is also making nice progress with his inflamed big left toe. Sweeney could go on a rehab assignment by the time the Red Sox return home from this road trip.