Israel finished bottom of Group D after losing to Serbia, Estonia and Bulgaria but had hoped to avoid the drop by beating Georgia.
Julia Glushko (193) won her singles match in the relegation play-off in Estonia, but Deniz Khazaniuk (246) lost her tie and Israel's fate was sealed when Glushko and Khazaniuk were beaten in the doubles.
Israel captain Tzipi Obziler said: "It was a tough week. We lost six close-fought three set matches and had just one of those matches gone our way we wouldn't be in this position."
Israel's Fed Cup team is struggling to adjust to life after Shahar Peer. The former world No.11, aged 29, has not officially announced her retirement but has not played in a tournament for nearly 12 months.