Aaron Ramsey also came off with an ankle injury at Old Trafford, but Emery said "it's smaller than Rob's" and that the Wales worldwide will also be assessed on Friday.
The injury to Holding is the latest defensive setback for Arsenal, who remain without centre-back Laurent Koscielny and left-back Nacho Monreal.
Neither man continued in central defence in last night's 2-2 draw against Arsenal, but Mourinho stuck with the same system he employed at St Mary's. Some of them had not played all season, Chris Smalling playing in very hard condition, but Arsenal were only unsafe when we lost the ball in bad areas. But the draw means Arsenal still haven't won in the league at Old Trafford since 2006, although they extended their current unbeaten streak to 20 games in all competitions.
The Gunners, buoyed by their north London derby win, threatened to leave Old Trafford with all three points and went ahead after a De Gea mistake that raised as many eyebrows as Mourinho's decision to drop Paul Pogba and Romelu Lukaku to the bench.
There is clearly much work to be done, but Darmian believes positives can be taken from a meeting with Arsenal that saw the Red Devils hit back on two occasions to claim a share of the spoils.
Harry Kane's ninth league goal of the season gave Tottenham an early lead and the Londoners struck twice early in the second half through Lucas Moura and Heung-Min Son.
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"The best news for me is [being] calm, but the doctors are looking at him and they are going to communicate with us". With the help of my team-mates, the coach and the fans I think I will be improving a lot here.
While Holding may be out for the long term, Emery said captain Laurent Koscielny could soon be ready to make his first start of the season - possibly in next week's Europa League match against Qarabag.
"We are waiting", Emery said.
"But good performances. I could speak about everyone".
"But I think my game can adapt and (I can) get my game together here and settle down".
"The only thing is about Huddersfield, the games happen very quickly for the players, for me, for us".
"There is a big difference in class but we knew that coming into this game".