The Ghana international, 31, had spells with Premier League sides Everton, Chelsea and Newcastle.
BBC reports Atsu had been missing since the 6 February quake that caused the collapse of his apartment in Antakya, Hatay.
"There are no words to describe our sadness," tweeted his Turkish top-flight club Hatayspor.
"We will not forget you, Atsu. Peace be upon you, beautiful person."
