Speaking in Istanbul, President Recep Tayyip Erdogan didn't mention by name the Syrian Kurdish People's Protection Units, or YPG, but said that those responsible will pay for it.
A spokesman for the Kurdish militia, Mustafa Bali, said his fighters downed the chopper in Raju, northwest Afrin.
But the Turkish prime minister said the cause of the helicopter's crash was not yet clear and investigations were ongoing.
"We don't have exact evidence or document to determine that it went down with any outside interference," Binali Yildirim told reporters in the western province of Mugla.
Turkey launched a military offensive on January 20 to oust the YPG from Afrin. Turkey considers the group an extension of an insurgency within its own borders.
Twenty one Turkish soldiers have died since the beginning of the operation.