Dortmund extended their lead at the top of the table back to nine points with a 2-1 victory at Signal Iduna Park, in what was their last match ahead of the German domestic winter break.
And they had to do it largely without talisman Alcacer, who has 12 Bundesliga goals to his name this season, after he came off in the 34th minute.
Alcacer was replaced by Mario Gotze, and goals from Jadon Sancho and Marco Reus earned Dortmund all three points.
"It looks like a torn muscle," sporting director Michael Zorc said in quotes reported by SID.
However, Zorc expects Alcacer will be available when Dortmund resume training on January 3rd.
Alcacer joined on loan from Barcelona in August. In November Dortmund exercised the option to sign him permanently for €23million on a five-year contract.
While the attacker has enjoyed a superb season he has strangely contributed most of his goals from the bench. Of his 12 league goals this campaign only two have been registered from starts, meaning he has netted a remarkable 10 goals coming off the bench.
Alcacer even bagged a hat-trick when coming on as a substitute against Augsburg in October.
Should the striker miss any Dortmund games after the winter break it will come as a real blow for manager Lucien Favre. Only Lionel Messi has registered more goals in Europe’s top five leagues this season than Alcacer.
His goals have ensured that Die Schwarzgelben are top of the table at Christmas, and are in pole position to win a first title since 2011/12, when Jurgen Klopp’s men managed to retain their title ahead of chasers Bayern Munich.
However, the Bavarian outfit have gone on to win the past six league titles.
Niko Kovac’s side would leapfrog Gladbach and move within six points of Dortmund if they beat Eintracht Frankfurt on Saturday.
Both Dortmund and Bayern are still alive in the DFB Pokal German Cup and the Champions League, with both facing meetings with English sides in the last 16, against Tottenham and Liverpool respectively.