The glamour model also claims people from ethnic minorities are "pushing their way to the top slowly slowly. Next will be a Muslim PM. And a black king".
Confronted by the paper about the remarks, the 25-year-old said they had been "taken out of context".
"I apologise unreservedly for the shocking language I used," she said in a statement.
"The opinions I expressed were deliberately exaggerated in order to make a point and have, to an extent, been taken out of context. Yet I fully recognise the offence they have caused."
In a statement last night Ukip chairman Paul Oakden said: "In light of messages that have been brought to my attention, I have taken the decision to immediately suspend her party membership pending an investigation. Ukip does not, has not and never will condone racism."
It piles more pressure on Mr Bolton, who has already attracted negative publicity by announcing he was leaving his second wife Tatiana Smurova for Ms Marney.
He has insisted he will not step down over the furore, saying it would "cripple" the party to replace their leader for the fifth time in under two years.