In a statement, Jo Marney apologized for the "shocking language" she used in a series of text messages to a friend, but said her words had been "taken out of context."
The Mail on Sunday newspaper reported that the 25-year-old Marney, who describes herself as a model and actor, made offensive comments about Markle and black people, including calling them "ugly."
UKIP leader Henry Bolton said Marney's membership in the party, known for its anti-European Union stance, was suspended immediately. Marney doesn't hold an official post in the party.
Markle, who will wed Harry in May, has spoken publicly and written about being proudly biracial, and also about how it affected her acting career.
Last year, Harry criticized some media reports and online comments for drawing negative attention to Markle's African-American heritage.
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.
Copyright 2018 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.