The statement described Mizrahi's remarks as "baseless" and contained "unacceptable claims and nonsense targeting our prime minister and our country."
The Turkish military also denounced Mizrahi's remarks, saying they "distort the realities and are excessive, unfortunate and unacceptable".
Such comments "can harm national interests in relations between the two countries," the military said in a statement.
"We expect the Israeli general staff, which we believe places importance on relations with the Turkish armed forces, to clarify the issue," it said.
In Jerusalem, the Israeli army later issued a statement saying Mizrahi's remarks were not representative of its views.
"General Mizrahi said some things that might be construed as critical of Turkey. The army spokesman wishes to clarify that this is not the official position of the army."
The Gaza conflict has strained relations between Israel and Turkey, a predominantly Muslim non-Arab nation which has been Israel's main regional ally since the two signed a military co-operation accord in 1996.
On January 29, Erdogan stormed out from a heated debate on the Gaza war at the World Economic Forum in Davos, Switzerland after clashing with Israeli President Shimon Peres.
Before walking off, he said Israel committed "barbarian" acts in Gaza, told Peres that "you know well how to kill people" and lashed out at the audience for applauding the Israeli president's emotional defence of the war.