The Red Devils ended a two-game losing run on Monday night thanks to a 3-0 victory over League One side Shrewsbury Town in the FA Cup fifth round.
Chris Smalling broke the deadlock in the 37th minute and Juan Mata added a second on the stroke of half-time before Jesse Lingard put the tie beyond doubt.
Schweinsteiger missed the FA Cup clash due to a knee problem which has kept the World Cup winner sidelined since January.
However, the 31-year-old was quick to offer his congratulations to his United team-mates following their FA Cup progression.
— Basti Schweinsteiger (@BSchweinsteiger) February 22, 2016
Louis van Gaal’s side will face Premier League rivals West Ham United at Old Trafford for a place in the FA Cup semi-finals.
United hosts Danish champions FC Midtjylland in the second leg of their Europa League last-32 tie at Old Trafford on Thursday night.
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