The Sun reported Price, 43, had sent an abusive message to her ex-husband Kieran Hayler and his fiancee, Michelle Penticost.
A spokeswoman for Sussex Police said: “At 5.45pm on Friday (January 21) police responded to a report that a suspect had breached their restraining order.
“Officers arrested a woman in her 40s who has been released under investigation while inquiries continue.”
Price was banned from contacting Penticost in 2019 under the terms of a five-year restraining order.
She was fined hundreds of pounds for hurling a foul-mouthed “tirade of abuse” at her during a row in a school playground.
In December, Price was handed a 16-week suspended sentence for drink-driving while she was disqualified and did not have insurance, as well as a two-year driving ban.
She was driving to visit a nearby friend in Sussex when the crash happened at about 6.20am on September 28.
Her representative has been contacted for comment.