Woodward played 20 games for the Mariners this season, hitting .239 with five RBIs, before being designated for assignment on Tuesday.
The 33-year-old Woodward had been at his home in Tampa, Fla., mulling his options when the call came from the Red Sox.
As long as Lowrie is out, Nick Green will get the bulk of the playing time at shortstop.
"Well, it's nice to be on one of the teams we didn't like playing [against]," Woodward said. "Obviously, the Yankees and Red Sox, it was kind of mentally taxing every time you'd go in there and play."
As for Lowrie, there was reasonably good news in that he seemed confident that his current condition isn't a sign that he is suffering any kind of setback from the surgery he had in April. If anything, it is probably just symptomatic of a player coming off that type of procedure.
"I talked to Dr. [Donald] Sheridan on the phone today, and it's obviously hard to diagnose, but it sounds like maybe some sort of neuritis where the nerves are inflamed and are shutting down the area," Lowrie said. "That's what I take from it."
Lowrie will consult with the training staff again on Saturday. He stayed away from baseball activities on Friday.
Woodward has played for the Blue Jays, Mets, Braves and Mariners. He is a career .243 hitter in 627 games, producing 33 homers and 191 RBIs.
Ian Browne is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.