Shaw, 20, received treatment on the pitch for 10 minutes after a tackle by PSV defender Hector Moreno in United’s first Champions League group game.
The England defender was given oxygen while he was taken off the pitch.
Shaw made 20 appearances for the Red Devils in an injury interrupted first season after joining from Southampton.
The player was inundated with messages of support on social media including from his former club.
And less than an hour after suffering the injury, he said: “Thank you everyone for your messages, words can’t describe how gutted I am, my road to recovery starts now, I will come back stronger.”