A police statement said the woman was a resident of southern Israel, and police said other details of the case were still subject to a court gag order.
The Bennett family received two death threats in the mail, including bullets.
In response, security measures were tightened around the Prime Minister and his family, and the police and the Shin Bet Internal Security Service opened an investigation.
Bennett, who leads a small nationalist party, has come under fire from Israeli hardliners who accuse him of abandoning his ideology.
Bennett leads a tenuous coalition of eight parties, ranging from a small Islamist party to ultra-nationalist Jewish nationalists, that have nothing in common other than their opposition to former Prime Minister Benjamin Netanyahu.
Bennett’s government was formed after four inconclusive parliamentary elections, which highlighted deep divisions in Israeli society over relations with the Palestinians, religion and the state, and Netanyahu’s eligibility to rule while on trial for corruption.
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