First baseman/outfielder Daniel Nava, who was optioned to Triple-A Pawtucket on Saturday to make room for Rubby De La Rosa, will likely be recalled and take Carp's roster spot.
Farrell said the fracture resulted from a pitch that hit Carp in the foot during the Red Sox's 6-3 win over the Braves on Tuesday. Carp went for a CT scan Sunday prior to the game, which revealed the injury.
Carp has posted a .214/.317/.286 slash line in 70 at-bats this season, driving in six runs while scoring eight.
Nava has struggled mightily this season after a strong 2013. His slash line this year is .130/.221/.234. Last season, it was .303/.385/.445 in 134 games.
"When Daniel's right, it's one of the purest left-handed swings we have," Farrell said. "He's still working back to gain that consistency."
Ian Browne is a reporter for MLB.com. Read his blog, Brownie Points, and follow him on Twitter @IanMBrowne. This story was not subject to the approval of Major League Baseball or its clubs.