The Germany international was a second-half substitute at the Etihad Stadium in Sunday’s derby as Louis van Gaal’s side secured bragging rights for the red half of Manchester.
Marcus Rashford scored his third goal in four Premier League games after he escaped the attentions of Martin Demichelis and placed his finish under England number one Joe Hart in the 16th minute.
United’s 1-0 win against their derby rivals left Van Gaal’s side in sixth place but the 20-time English champions are just one points adrift of fourth-placed City.
World Cup winner Schweinsteiger took to Instagram to continue to savour their derby day success on Monday afternoon ahead of the international break.
Schweinsteiger wrote on the photo-sharing app: “Still happy about yesterday’s derby win. Have a great start into the week! #mufc”
The 31-year-old moved to United in a £6.7m deal from German champions Bayern Munich last summer.
Schweinsteiger has scored one goal in 18 Premier League appearances so far this season.
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