Saturday's goalless draw at Old Trafford was overshadowed by the incident in which Germany international Schweinsteiger appeared to strike the New Zealand centre-back with his forearm.
Referee Mark Clattenburg and his assistants missed the altercation and the FA have subsequently opted to take retrospective action for an "alleged act of violent conduct".
An FA statement read: "Bastian Schweinsteiger has been charged for an alleged act of violent conduct which was not seen by the match officials but caught on video.
"The Manchester United midfielder was involved in an incident with West Ham United’s Winston Reid in the 40th minute of the game on Saturday 5 December 2015.
"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."
