Rashford received online racial abuse in January after United's 0-0 Premier League draw against Arsenal and said he was subject to similar comments again, prompting the forward to call them out.
The England international said he had seen "at least 70 racial slurs" on his social media account following the defeat.
"At least 70 racial slurs on my social accounts counted so far," Rashford wrote on Twitter. "For those working to make me feel any worse than I already do, good luck trying."
United swiftly backed Rashford, condemning the racial abuse on social media.
At least 70 racial slurs on my social accounts counted so far. For those working to make me feel any worse than I already do, good luck trying 👍🏾— Marcus Rashford MBE (@MarcusRashford) May 26, 2021
"Following the #UEL final, our players were subjected to disgraceful racist abuse," the official United account tweeted. "If you see any form of abuse or discrimination, act and report it."
After the racial abuse in January, Rashford described the slurs as society at its worst.
"Humanity and social media at its worst. Yes I'm a black man and I live every day proud that I am," Rashford wrote on Twitter at the time.
"No one, or no one comment, is going to make me feel any different. So sorry if you were looking for a strong reaction, you're just simply not going to get it here.
"I'm not sharing screenshots. It would be irresponsible to do so and as you can imagine there's nothing original in them.
"I have beautiful children of all colours following me and they don't need to read it. Beautiful colours that should only be celebrated."