In 540 at-bats over the last two seasons, Craig hit .206 with nine homers, 49 RBIs and an on-base/slugging line of .273/.298.
The right-handed hitter has a balance of $21 million remaining on his contract over the next two seasons, making it extremely unlikely the Red Sox can trade him without absorbing almost all of the cost. That figure includes a $1 million buyout of Craig's club option for 2018.
Righty relievers Jean Machi and Alexi Ogando were both outrighted from the Major League roster and will become free agents.
Catcher Sandy Leon signed a one-year Major League contract for next season and was outrighted to Pawtucket.
In addition, right-hander Clay Buchholz, closer Koji Uehara, catcher Christian Vazquez and righty relievers Anthony Varvaro and Brandon Workman were reinstated from the 60-day disabled list.
Boston's 40-man roster is now at 38.
Ian Browne is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.