The FA announced it had charged the German on Monday over the incident, which occurred in United's 0-0 draw against West Ham on Saturday.
Schweinsteiger stuck out his left arm and caught Hammers defender Reid in the throat as both players jostled for position in the build-up to a first-half free-kick.
Referee Mark Clattenburg spoke to both players to calm them down, but did not see the apparent elbow and it was therefore not mentioned in his post-match report.
That left the FA free to punish the midfielder retrospectively.
Schweinsteiger does not think his actions warrant punishment, however, and has informed the club he wishes to contest the charge.
United have until noon on Thursday to lodge an appeal.
The 31-year-old is facing a three-match ban if found guilty.
Already hampered by a lengthy injury list, United cannot afford to lose the influential player for their upcoming games against Bournemouth, Norwich and Stoke.
Reid insisted on Saturday that the elbow was intentional.
"He knows what he's done - he's elbowed me in the face," the New Zealand centre-back said after the game.
And West Ham manager Slaven Bilic claimed the player should have been sent off.
He said: "It's a clear red card
A straight red without any doubts
It was a moment of madness.
"He deserved to be sent off, but the referee told me he didn't see it
Fair enough, I believe it
It was an elbow."
Source : PA
Source: PA