Men aged between 18 and 40 years who plan to travel to the two countries need prior clearance from Egyptian immigration under the new rules which came into effect on December 3.
"We are adopting these measures to protect our sons from joining terrorist groups abroad," the official said. "Now every man travelling to these countries must clearly state the reason to the authorities."
Militants have stepped up attacks in Egypt, mostly in the Sinai Peninsula, since the ouster of Islamist president Mohamed Morsi last year, and officials say that many of them have fought in Syria, which borders Turkey.
In November Egypt's deadliest militant group, Ansar Beit al-Maqdis, pledged allegiance to the Islamic State group, further raising security concerns.
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Egyptian militants say their attacks are in retaliation for a bloody government crackdown against Morsi supporters that has left at least 1,400 people dead and thousands jailed.
Morsi's Muslim Brotherhood movement has been designated by the authorities as a "terrorist group".
Ties between Cairo and Ankara have deteriorated since the army ousted Morsi, a key ally of Turkey.
Egypt has accused Ankara of "backing terrorism," while Turkey has dubbed Morsi's ouster a "coup".
Turkey, a vocal critic of the regime of Syrian President Bashar al-Assad, has denied accusations that it tolerates the flow of foreign fighters into Syria.
Cairo has also regularly raised concerns over the war in Libya, which has plunged into chaos since the ouster and killing of long-time leader Moamer Kadhafi in 2011.