Rob Bradford of WEEI noted Nunez was hurt while running to first base. Sean McAdam of the Boston Sports Journal added the veteran infielder couldn't put any weight on his leg and had to get carried off the field at Minute Maid Park in Houston.
He'd previously been sidelined by a knee injury for most of September. It wasn't immediately clear whether the two ailments are directly related.
Boston manager John Farrell said the lingering effects of the previous issue would likely limit where Nunez could play in the field throughout the American League Division Series.
"Getting his bat back in the lineup will be a plus but initially it would be at those two positions: second and third," he told reporters. "At this point, we kind of feel like that's the best defensive capability and range right now."
The Red Sox acquired the 30-year-old Dominican Republic native from the San Francisco Giants in July in exchange for pitching prospects Shaun Anderson and Gregory Santos.
Nunez, a 2016 All-Star Game selection, provided a boost to the offense during the stretch run of the regular season. He posted a .321/.353/.539 triple-slash line with eight home runs and six stolen bases in 38 games following the trade.
His value is enhanced by the ability to play multiple positions. He appeared at second base, shortstop and third base with Boston and also has experience at the corner outfield spots.
It's unknown how long Nunez could be out after leaving Thursday's game. Hanley Ramirez will likely serve as the team's full-time DH in his absence.