The Netherlands international was hurt during last weekend's 2-1 loss at Swansea City and was later pictured leaving the Liberty Stadium with a protective boot.
Manager Louis van Gaal has subsequently confirmed Van Persie will be unavailable against Gus Poyet's men, and suggested Van Persie could be absent for at least the next two weeks.
"He is injured," said Van Gaal. "It is an ankle problem. I do not think it is very heavy but ankle problems can take a long time.
"It is not one or two weeks."
He added on the club's official website: "Van Persie is the only injured player. We will have to wait and see how long that shall take."
There was better news for United, however, with midfielder Michael Carrick nearing a return after a near month-long absence with a muscle rupture.
The England international has rejoined training, but Van Gaal is keen to ease him back into action.
"Carrick trained yesterday for the first time with the group," he added. "He is very experienced and he can play in a very important position.
"But he also needs match rhythm. He trained only one time with us, with the group so he needs to also play in the second team."
