Rashford received the discriminatory messages after featuring in Manchester United’s goalless draw game against Arsenal in the Premier League on Saturday.
The 23-year-old England international is the third United player to be subjected to racist abuse online in less than a week after Anthony Martial and Axel Tuanzebe endured similar vilification following the Red Devils’ shock 2-1 home loss to bottom side Sheffield United in the Premier League on Wednesday.
Chelsea defender Reece James also revealed on Friday that he had been sent racist messages on social media.
"Humanity and social media at its worst. Yes, I’m a black man and I live every day proud that I am. 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," Rashford wrote on Twitter.
"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."
Rashford has scored 15 goals in 33 appearances across all competitions for Ole Gunnar Solskjaer’s men this season.