The German midfielder is reported to have elbowed Hammers defender Winston Reid during the first half of the Old Trafford encounter.
The incident escaped the attention of Mark Clattenburg but has since been picked up retrospectively, as stated by the FA.
"Bastian Schweinsteiger has been charged for an alleged act of violent conduct which was not seen by the match officials but caught on video," read the FA statement.
"The matter was referred to a panel of three former elite referees who each reviewed the video footage independently of one another to determine whether they considered it a sending-off offence.
"For an FA charge to follow the decision by the panel must be unanimous. The player has until 12 noon on Thursday 10 December 2015 to reply to the charge."
If found guilty, Schweinsteiger could be hit with a three-match suspension.