Turkaslan was the victim of one of many collapsed buildings in Turkey, the team said.
"Our goalkeeper, Ahmet Eyup Turkaslan, lost his life after being under the collapse of the earthquake," wrote the club on social media. "Rest in peace. We will not forget you, beautiful person."
Turkaslan spent his entire senior career at Turkish clubs, including Bugsasspor, Osmanlispor, Umraniyespor and Yeni Malatyaspor. He is survived by his wife, Kubra Turkaslan, who escaped the rubble, according to a statement she made to local media.
The death toll from the 7.8-magnitude earthquake that affected Turkey and Syria has surpassed 5,000 as of Tuesday afternoon and is expected to rise as more bodies are located.
All professional football matches in Turkey have been postponed indefinitely amid the humanitarian crisis.