The artwork which honours the footballer in Withington, Manchester, was defaced following England’s defeat at Wembley Stadium.
Manchester locals have, however, covered up the graffiti and instead placed messages of support on the mural. One message reads “hero”, with another saying “role model”.
Rashford missed his penalty on Sunday night while Jadon Sancho and Bukayo Saka had their spot kicks saved by Gianluigi Donnarumma.
Greater Manchester Police have launched an investigation after the “racially aggravated damage” was reported to officers in the early hours of Monday morning.
“Hate crime in any form is completely unacceptable and not welcome here in our city.”
The FA has also condemned the racist online abuse suffered by Rashford, Sancho and Saka.