The ban begins with immediate effect after the Germany captain accepted an FA charge for violent conduct. The incident, last Saturday at Old Trafford, was not seen by the match officials but was caught on video.
Schweinsteiger caught Reid in the throat as the players battled for position from a first-half free-kick during the 0-0 draw.
He will miss the forthcoming Premier League games against Bournemouth, Norwich City and Stoke City.
Hammers defender Reid said after the match: “It was a red card. He knows what he’s done – he’s elbowed me in the face. The referee couldn’t see it, so we move on.”
West Ham boss Slaven Bilic told Sky Sports: “It is a red card, but I can agree that he didn’t see it. No matter how many referees you have, sometimes they can’t see.
“I’m sure if he did see it, it would have been a straight red. Of course we are disappointed but it happens. He just didn’t see it.”