Craig's service time means he must accept the assignment.
PawSox outfielder Jackie Bradley Jr. was a late scratch ahead of Saturday's contest against Columbus.
Bradley was slated to lead off and play center field, but the club swapped him out for Quintin Berry a few hours later, possibly indicating that Bradley is on his way to join the Red Sox
The 25-year-old is hitting .343 (34-for-99) with one homer in 24 games for Pawtucket. He's yet to appear in a game with the Red Sox this year.
Craig has struggled in 2015. In 23 games, he's hitting .146 (7-for-48) with one homer.
Originally acquired from the Cardinals in a trade for John Lackey, Craig has been unable to recapture his 2013 form, when he hit .315 with 13 home runs and a career-high 97 RBIs.
Red Sox manager John Farrell suggested following his team's seventh loss in its past eight games that a roster shakeup could be on the way.
Since going 3-0-1 in their first four series, the Red Sox are 1-5-0 in their past six.
Jamie Ross is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.