Manager Alex Cora said after Thursday's loss that there's "a strong possibility" Martinez will be in the starting lineup for Friday's Game 2, but he made no guarantees.
Martinez also missed Tuesday night's win over the New York Yankees in the AL Wild Card Game because of a sprained left ankle.
Martinez stumbled over second base while heading to the outfield in Sunday's regular-season finale at Washington.
Because the National League does not use a DH in games played in its stadiums, Martinez was playing right field against the Nationals. He stepped on the bag and twisted the ankle heading out to play defense in the fifth inning.
It was only the seventh game in 2021 that Martinez started in right field. He was in the starting lineup as a DH for 113 games and as the left fielder for 28.
Martinez hit .286 with an AL-leading 42 doubles and 28 homers and 99 RBIs during the regular season.
Rays manager Kevin Cash said he planned to be aggressive in using his bullpen during the series. He said right-hander Drew Rasmussen will start Game 3 or 4, with the other contest being a bullpen day.
Sale made nine starts this year after having Tommy John surgery on March 30, 2020.
"It's been two years trying to get to this point," Cora said. "All the hard work, all the tears and sweat throughout the process. So we have to take care of him, but it was his turn and we feel comfortable with him."
Sale said he would be available to work as a reliever later in the series as well.
"There's no reason to save an arm to go sit on the couch, you know what I mean?" Sale said. "This is all the baseball we have left, and we're going to get certain points in these series where tomorrow might not come. So if that's the case and it's what's called upon, you know, it's my job."
Red Sox right-hander Matt Barnes, who lost his closer role in August, was not on the roster after being active for the wild-card game. Others dropped were catcher Connor Wong, infielder Jonathan Arauz and outfielder Jarren Duran.
Boston outrighted infielder Jose Iglesias to Triple-A Worcester, reinstated infielder-outfielder Yairo Munoz from the COVID-19 injured list and outrighted him to Worcester on Wednesday. Iglesias was not eligible for the postseason roster because he signed with the team after the Aug. 31 cutoff.
Nick Anderson, Tampa Bay's closer during its run to the World Series last year, failed to make the roster. He didn't make his 2021 debut until Sept. 13 because of a right elbow injury and struggled in six late-season appearances.
With Boston having several left-handed starting pitchers on its roster, Tampa Bay added right-handed-hitting outfielder Jordan Luplow.
The AL East champion Rays lost the World Series in six games to the Los Angeles Dodgers in 2020.
The Associated Press contributed to this report.