The 21-year-old came off during the latter stages of the Premier League clash.
The left-back went into the Manchester derby with something of a question mark over his fitness after withdrawing from the England squad that beat Slovakia last week.
Shaw was replaced by Anthony Martial in the latter stages of the game
However, he managed to get over 80 minutes under his belt against Pep Guardiola's men before he was replaced by Anthony Martial as United chased the game.
But the Manchester Evening News is now claiming that he suffered an injury and is expected to be left out for the trip to the Netherlands to give him the best chance of being ready for the game against Watford at Vicarage Road next weekend.
Manchester United manager Jose Mourinho
Though Shaw has established himself as an important player for the Red Devils since his return from the long-term injury that he picked up last season - coincidentally, coming in a European game played in the same country that Jose Mourinho's men will be travelling to this week - United have enough cover to suggest that even if he had been fit, he would not have started anyway.
Both Matteo Darmian and Marcos Rojo could be contenders to take his place in the side as Mourinho may want to keep his first-choice options fresh for the weekend.