Recalling Barnes restores the Red Sox's bullpen to seven arms after the club designated Edward Mujica for assignment Thursday.
Manager John Farrell said Barnes gives the team a power pitcher who can go multiple innings.
"What we're not going to be doing is bouncing him back and forth at this level, between starting and relieving," Farrell said of Barnes, who is ranked as the Red Sox's No. 9 prospect by MLB.com.
The 24-year-old has made three starts (four appearances) with the PawSox this season, allowing six earned runs over 13 innings. He's made one relief appearance for the Red Sox in 2015, tossing two scoreless innings against Baltimore on April 25.
Outfielder Shane Victorino (15-day DL, hamstring strain) was scheduled to continue his rehab assignment Saturday at Double-A Portland. Farrell said he expected Victorino to rejoin the Red Sox on Sunday before being activated Monday, when the club opens a series in Oakland.