Miss Brown had already been receiving unpleasant comments on the micro-blogging site but it was when they took a more serious turn last week that web moderators decided to report the matter as a crime.
The 20-year-old, who is from London, is one of the favourites to win the show, and has been compared by judges to Aretha Franklin, Tina Turner and Mariah Carey.
She has described those behind the remarks on her Twitter page as "warped".
The singer has a huge following on the site, many of whom offered their support after the unpleasant remarks were posted.
Some tweets described her as an "ugly fat cow", the "fat controller" and "fat wasp", after she wore a yellow and black dress on last week's show.
But Miss Brown took the comments in her stride, retweeting them to her online followers, adding: "OK I'm big, get over it."
The BBC confirmed yesterday that an alleged crime was reported last week when staff working for the online team for The Voice's production company, Wall to Wall, became concerned about racist content in some messages.
Executives at the corporation took the view that while it was inevitable that there would be negative and sometimes unpleasant comments posted, these particular remarks were much more serious and potentially illegal.
The racist comments appear to have been removed from the site although some other offensive remarks remain.
Miss Brown told a Sunday newspaper: "There are so many warped people out there who want to cause upset.
"Not only have I endured jibes of a racial nature but sick comments about my weight. Things have been said about my dad too."
In the interview with The People, she added that she had at first cried about the remarks but then decided to speak out "to encourage other people to fight out against the bullies".