Yankees manager Joe Girardi said that Rodriguez will rejoin the team on Tuesday in Boston but added that it is "really questionable" whether Rodriguez would be available to play in the three-game showdown.
"He's day to day -- I don't know if he'll be able to play," Girardi said. "With his thumb, you've got to let it heal, so I can't tell you exactly when he's going to be back. It's just when he feels better."
Rodriguez originally sprained his thumb while stopping a Joe Mauer infield single in Minnesota on Aug. 21, his first game back from a stint on the disabled list.
Rodriguez aggravated his thumb injury in the first game of Sunday's doubleheader against the Orioles, going 0-for-4 at the plate, and did not speak to reporters after the games. Hand specialist Melvin Rosenwasser saw Rodriguez in New York.
"He came back and he said he irritated it a little bit more, so we just have to be smart about it," Girardi said.
Rodriguez has played in just four games since coming off the DL from surgery to repair a torn right meniscus, going 3-for-17 (.176) with a home run.
"You'd like to give him some continuity," Girardi said. "You figure your timing gets better the more at-bats you have in a row, and his have been broken up. It's just something we're going to have to deal with."