The soldiers were detained during a huge search operation in the area around the Aegean Sea resort of Marmaris targeting those behind the attack. Four more soldiers are still on the run, the report said.
The three were detained during a traffic check in the Cetibeli district of Marmaris and have been taken to a police station for questioning.
The attack on Erdogan's hotel, where he was vacationing with family members including his son-in-law, Energy Minister Berat Albayrak, came shortly after he had left the resort by plane for Istanbul.
The Dogan news agency published a picture of the three in the back of a police van, looking bedraggled after 10 days on the run.