The singer – who is nominated for the 2014 Mercury Prize and three MOBOs – said she was "disgusted" by the offensive comments shared on Twitter.
"I am genuinely shocked and disgusted at the amount of racism that has been infecting my account the past week," she wrote.
"Racism is unacceptable in the real world and it's unacceptable online."
Her debut album, LP1, was released in August this year, and she has numerous UK gig dates planned starting on 3 October in Birmingham.
Racism is unacceptable in the real world and it's unacceptable online.; FKA twigs (@FKAtwigs) September 28, 2014
I am genuinely shocked and disgusted at the amount of racism that has been infecting my account the past week.; FKA twigs (@FKAtwigs) September 28, 2014
Although their relationship has not been confirmed, fans of Pattinson have voiced their grievances at the actor having a new girlfriend in a series of tweets.
Others are seemingly aggrieved that he is no longer dating his ex-girlfriend, Kristen Stewart.
Twigs, real name Tahliah Debrett Barnett, was born in Gloucestershire and is now based in London. Her father is Jamaican and her mother is part English, part Spanish.
She was the only mixed-race student at her Catholic school and remembers her appearance being the subject of scrutiny.
"Obviously it was hard," she said in a recent interview with Dazed and Confused.
"People said horrible things about something I had no control of, which was tough. But that’s okay. Life isn’t supposed to be easy, is it? I never really saw anything wrong with how I looked, it was more that certain people pointed things out to you about yourself.
"Either your hair’s different, or the colour of your skin, or your features. Half of my life I’ve had people staring at me because they think I’m funny-looking and ugly. The other half of my life I’ve had people staring at me because they think I’m fascinating. Everything neutralises. It’s more of a statement on society and how weird it is."