Gunmen stormed a bar in the village of Gbale in the state of Kwara and seized the men on Saturday, national police spokesman Frank Mba told AFP.
"We are working frantically to secure their release," he added.
Mba did not say if any ransom demands have been made.
Local media said the Turks were working for a construction firm in the state.
Kidnapping for ransom is common in Nigeria, especially in the oil-rich south and the northwest.
The victims are usually released after a ransom is paid although police rarely confirm if money changes hands.
Earlier this month, two Chinese nationals were kidnapped in the southern state of Edo.
Nigerian police could not confirm if they are still being held.
There have also been many abductions in the northeast, where an insurgency led by Boko Haram militants has killed 27,000 people and forced some two million to flee their homes since 2009.