Manchester United's medical bulletin shows no signs of improving, with Marcos Rojo dislocating his shoulder in training on Wednesday.
It is another setback for manager Louis van Gaal, whose defence has been ravaged with injury problems this season.
Left-sided Argentina international Rojo, signed from Sporting Lisbon for £16m in 2014, was hurt during a midweek training session, dislocating the same shoulder he damaged against Manchester City last season.
On that occasion, the 25-year-old did not have surgery but still missed four weeks and Van Gaal admitted he is unsure how many games Rojo will be out for.
Speaking at his weekly press conference, Van Gaal said: "He (Rojo) dislocated his shoulder which is more or less the same thing that happened last season, meaning he is out for more weeks.
"The question as to whether he shall be operated is a question for the doctor and for Marcos."
Rojo's absence leaves Van Gaal short of options at the back, with Luke Shaw a long-term problem after suffering a double leg break against PSV Eindhoven in September.
Makeshift right-back Antonio Valencia is also out after undergoing surgery on his foot.
Rojo was out of favour with Van Gaal at the start of the Premier League campaign after missing the pre-season tour of the United States, but has impressed at left-back in recent weeks.
With United welcoming West Ham on Saturday, Rojo's injury may see Daley Blind moved from the heart of defence to left-back, while Van Gaal admitted his growing injury list could force him to enter the transfer market for a defender in January.
"They are always contact injuries and you cannot afford that," Van Gaal said. "We have a lot of contact injuries and also long-lasting injuries so that's our problem.
"So we are looking [at players for January] but as you know it is not so easy to buy players and in January it is more difficult. We are looking but it is not for sure."