The German international caught the Hammers centre back in the face with his left arm as they jostled before a free-kick in the 40th minute of Saturday’s goalless Premier League draw.
Schweinsteiger will be banned for three games if found guilty and has until 1200 GMT on Thursday to respond to the charge.
Referee Mark Clattenburg spoke to both players after the incident but did not include it in his match report.
“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 FA said in a statement on its website.
“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.”