The Mail on Sunday newspaper reported that the 25-year-old Marney made offensive comments about Markle and black people, including calling them "ugly".
In a statement to the MoS Ms Marney said she apologised "unreservedly" for the "shocking language" she used in the messages.
Ukip leader, Henry Bolton, who's relationship with Jo is under investigation by the party, confirmed that she was "immediately" suspended following the claims.
Nuttall resigned after seven months following the Election, when Ukip's polled less than 2 per cent. Steve Crowther took over until Mr Bolton was elected in September. "He must go, he must go quickly, he must go as quietly as possible".
Ms Marney wrote that Ms Markle, a USA actress whose mother is black and father is white, will "taint" the royal family, the paper quoted one of her messages as saying.
Peter Whittle, a UKIP member of the London Assembly, tweeted: "These are disgraceful remarks".
"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".More news: January 2018 Nintendo Direct Mini Covers Upcoming Switch Games
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The prince issued a strongly worded statement condemning the "outright sexism and racism" in some comments about Markle, and said some articles with "racial undertones" crossed the line.
In the wake of the controversy, former Ukip leadership candidate Ben Walker has called for Mr Bolton to resign, accusing him of having "deeply flawed judgement".
Mr Bolton earlier replied to a party member online who urged him to call for Ms Marney to have her membership removed.
Ukip's National Executive Committee is set to meet on Thursday to decide the party leader's fate. The opinions I expressed were deliberately exaggerated in order to make a point and have, to an extent, been taken out of context.
On her Twitter profile Marney describes herself as a model, actor and journalist, as well as a Brexiteer.
He said he had already made clear on social media that he had recently been spending time "with somebody who has become increasingly important to me".
THE glamour model girlfriend of Ukip's chief was last night accused of sending a series of racist tweets about Meghan Markle.
Mr Oakden declined to give his own views on Mr Bolton's situation, but said the party needs to be "behind our leader 100% in taking that battle (for Brexit) forward".