Roberts wrote on social network Twitter: "I am truly sorry to all those upset... No harm was intended...."
The column was discontinued with immediate effect after the Sunday World and its owner Avusa Media acknowledged the outcry over the column, headlined 'Jou Ma se Kinders'.
In her column, Roberts remarked that coloured girls were the future "for various reasons".
"You will never run out of cigarettes," she wrote.
"You will always be assured of a large family as many of these girls breed as if Allan Boesak sent them on a mission to increase the coloured race.
"They are the closest thing to being a white woman and we know you black men love them as they look like they've popped out of an Usher music video."
"They have no front teeth and eat fish like they are trying to deplete the ocean" and "they love to fight in public and most are very violent," she continued.
Sunday World editor Wally Mbhele said the column, which is being investigated by the SA Human Rights Commission, made derogatory generalisations about coloured people which were in clear violation of the SA Press Code and Avusa Media's internal codes.
Mbhele said he took full responsibility "for the offending column appearing in my newspaper".
Avusa Media editor-in-chief Mondli Makhanya said the company had already begun an internal inquiry into the matter.
Roberts' column comes amid a furore over remarks made about coloureds by government spokesman Jimmy Manyi.
Manyi, then the director-general of labour, said in a show broadcast on KykNet's Robinson Regstreeks in March 2010 that there was an "over supply" of coloureds in the Western Cape.
The ANC distanced itself from Manyi's remarks, saying they were "disturbing" and "unacceptable", while Cosatu said the comments would inflame fears within the coloured community.
Government Communication and Information System (GCIS) deputy chief executive officer Vusi Mona has since apologised for the remarks on Manyi's behalf.