Interim manager Ole Gunnar Solskjaer could have as many as 10 players absent for the Premier League clash - and he confirmed the Frenchman would be one of them.
It means the Norwegian will call on reinforcemets from the club's academy ranks.
Midfielders Ander Herrera, Juan Mata and Jesse Lingard limped off during the 0-0 draw with Liverpool on Sunday, and striker Marcus Rashford hobbled through the game after picking up an ankle knock.
Solskjaer was already without midfielder Nemanja Matic and Martial, who has a groin injury.
"Martial is not going to be ready for this one, either, we can't risk it," said Solskjaer ahead of the trip to south London.
"So, maybe [he will be ready for] Southampton [at Old Trafford on Saturday], but we're not going to risk another one.
"In hindsight, Jesse was eager, he ticked all the boxes in training, with his recovery work and rehab, but maybe a couple of days too early. It was Liverpool and he was desperate to be part of it."
Defenders Phil Jones, Matteo Darmian and Antonio Valencia are also on the missing list.
Solskjaer added: "I don't know the list [of players] that's supposed to be injured, Matteo [Darmian] trained the other day, I don't think he'll be ready, [Marcos] Rojo will be involved, Rashy we're still waiting to see how his ankle is responding to the treatment, muscle injuries are too early to think about. That's it.
"Phil was ill one of the days last week, so he's been out for a little while as well with an illness.
"Luckily at centre-back there are quite a few fit ones, Victor [Lindelof], Chris [Smalling] and Eric [Bailly], the three of them are ready."
Young striker Mason Greenwood, who Solskjaer has hinted is close to getting a first-team chance, is also injured.
“The kids are joining in [training] today," said Solskjaer. "They’ll be involved in the squad.
"They’ve been part of our training for a long time now and I’m sure Angel has been successful with England’s Under-17s, the 2017 team with Sancho, Foden and Hudson-Odoi, so he’s been a big part of that. I’m definitely sure that if he gets a chance he’ll do well.
“James Garner is a Michael Carrick but 20 years younger, I’m sure he’ll do well and Chongy will be taking people on if he comes on. They’re ready, they’re kids.
"It’s hard if you’re a defender coming on if you’re 16 or 17 but as an attacker you go out there and express yourself, and there’s your chance. They can win you the game, not lose it for you.”