"Such remarks don't deserve a response," ministry spokesman Badr Abdel-Ati said in a statement, a copy of which was obtained by Anadolu Agency.
Abdel-Ati went on to say that "the voice of the Egyptian people is the source of legitimacy" and their will "will define the future of the state."
Erdogan had earlier said he would "not recognize anyone elected as Egypt's president" in light of last summer's ouster of Mohamed Morsi – a move the Turkish prime minister sees as a "military coup" – by the army.
Relations between Cairo and Ankara have cooled since the army ousted Morsi, Egypt's first democratically elected president, last July.
Last November, the two countries downgraded their diplomatic relations.