"I am genuinely shocked and disgusted at the amount of racism that has been infecting my account the past week." the 26-year-old tweeted to her followers on Monday
FKA Twigs performs in 2014
She added: "Racism is unacceptable in the real world and it's unacceptable online."
The singer was first spotted with Twilight actor Robert in August, and in recent weeks the pair have taken their relationship public and have been photographed holding hands.
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
Racism is unacceptable in the real world and it's unacceptable online.— FKA twigs (@FKAtwigs) September 28, 2014
Robert, 28, had a high profile relationship with his Twilight co-star Kristen Stewart. It is thought that many of the tweets FKA Twigs has been receiving have been from fans unhappy that Robert has moved on since him and Kristen separated for good in 2013.
Speaking to the BBC, FKA Twigs, whose real name is Talilah Debrett Barnett, said: "I don't want to be a famous person. Up until now I've been able to hold back but now I understand I am releasing an album I have to give more of myself."
Robert Pattinson and FKA Twigs were first spotted together in the East Village
She continued: "Ultimately if you want to be blessed with such a wonderful career where you are basically your own boss. There is always going to be that sacrifice and that is the ultimate sacrifice."
The abuse comes weeks after FKA Twigs was nominated for the coveted Barclaycard Mercury Prize following the release of her debut album LP1.
Tahliah joined fellow nominees Kate Tempest, Anna Calvi and Nick Mulvey at the awards launch party to accept the nomination, and will find out if she has won the Mercury Prize 2014 when the awards show takes place at London's Roundhouse on Wednesday 29 October.