It was not immediately clear what caused the blast which occurred in Antalya's harbour area around 2pm (1100 GMT), assistant police chief Mujdat Ozcan said on Monday.
"It is not known what caused the explosion, whether there is a terrorist dimension," Ozcan said.
A teenager was killed in the explosion, while a 14-year-old Turkish boy who was injured at the scene was being treated at a local hospital, the state-run Anatolian news agency said.
The agency also said two suspects had been detained while the assistant police chief said one suspect was apprehended near the scene.
Television pictures showed police examining yachts docked in the harbour.
Turkey is on edge after a series of bomb attacks in recent months and is determined to maintain "stability" in order to gain EU membership.
Kurdish separatists and leftist groups have claimed responsibility for attacks that have mainly taken place in Istanbul and the capital Ankara.
Simultaneous bomb attacks rocked two hotels in Istanbul's popular Sultanahmet district earlier this month, killing a Turk and an Iranian and injuring 11 others, including foreign tourists.