The Red Devils and the other "big six" in England attempted to join a breakaway tournament that initially involved a total of 12 European teams.
The six English sides have since backed out of the tournament, while the entire Super League may collapse in the coming days.
Rashford tweeted a photograph with a quote from club legend Sir Matt Busby on Tuesday, before the news of United's withdrawal.
The Busby quote, which is among the current banners at Old Trafford, reads: "Football is nothing without fans."
— Marcus Rashford MBE (@MarcusRashford) April 20, 2021