The prosecutor said there were no grounds for prosecution after the Justice Ministry refused it permission to bring charges, the report said.
Turkish law allows for the trial of people accused of genocide or crimes against humanity even if the crimes were committed abroad, but says prosecutors need the ministry's permission before they can go ahead.
The investigation was launched in February upon a complaint by the Islamist- leaning human rights association Mazlum-Der accusing Israel of carrying out " direct attacks on civilians with the aim of annihilating them."
Mazlum-Der had asked that several Israeli officials, including President Shimon Peres and several ministers, be tried.
Israel's 22-day offensive on Islamist Hamas-controlled Gaza in December and January left more than 1,300 Palestinians dead and 5,300 others injured.
Thirteen Israelis were killed during the operation, which was launched with the declared aim of stopping rocket attacks on southern Israel by Palestinian militants.
The Gaza conflict has strained relations between Israel and Turkey, a predominantly Muslim non-Arab nation which has been the Jewish state's main regional ally since a military cooperation accord in 1996.
In January, Turkish Prime Minister Recep Tayyip Erdogan stormed out of a heated debate on the Gaza war at the World Economic Forum in Davos after accusing the Jewish state of "barbarian" acts against the Palestinians.