Napoli was dealt to the Texas Rangers on Friday night for a player to be named or cash. Boston also sent money to Texas as part of the deal, which came a week after baseball's deadline for trading players without placing them on waivers.
The 24-year-old Marrero is in his second major league stint. The first came earlier this season, when he appeared in five games and went 1 for 7.
Marrero was hitting .237 with five home runs and 22 RBIs for Pawtucket.