The Consumer Protection and Fair Trade Authority said in a statement it had questioned the head of Apple in Israel, Rony Friedman.
A spokesman at the Authority said it had the power to levy significant fines in civil proceedings, but that it was too early to discuss such a possibility.
A spokesman for Apple in Israel declined to comment.
Critics say Apple has obfuscated the fact that a worn-out battery not only fails to hold a charge but also degrades the phone's performance - and that this lack of transparency has pushed people to buy a new phone rather than a new battery.
Government agencies in countries ranging from Brazil to France and Italy to South Korea are also investigating Apple following complaints.
© Thomson Reuters 2018