The 29-year-old Scotland international, in his second season-long loan spell at the Terrors from Reading, was injured during the Premier Sports Cup defeat to Hibs at Tannadice last month.
McNulty has made six appearances so far this season but has yet to find the net. He last scored in a 3-0 win over Aberdeen in a Scottish Cup quarter-final in April.
Before Saturday's trip to Hibs in the cinch Premiership, Courts said: "After the game Marc McNulty had to undergo some minor surgery so it looks like he is going to be out for a period of time.
"But his rehabilitation will happen with Dundee United so our medical team are working on that rehab just now and hopefully we will have him back just before the new year.
"It was really disappointing because Marc was performing really well for us and I think it was only a matter of time before the goals were coming because he was performing at such a good level.
"So yes, it was disappointing but the feedback we have had from the surgeon and medical team is that it was a clean operation and he will be back fighting fit, hopefully around the new year."
McNulty, whose Reading contract expires at the end of the current season, scored five goals in 30 games for United in the 2020-21 campaign.
He also had two separate loan spells with Hibs in 2019 and 2020, either side of a stint at Sunderland.