Madonna is in Israel for concerts on Tuesday and Wednesday.
Livni's spokesman Gil Messing says the two women dined for more than two hours late Monday at the singer's request.
Both wore short-sleeved black dresses and embraced as they emerged from a Tel Aviv restaurant.
Messing says the pair decided to keep the content of the conversation private. He said Livni "was very impressed with Madonna and found her to be a very interesting person."
Messing said Tuesday that Livni and her husband plan to attend one of Madonna's show, the last on her current world tour.