Gelashvili is a surname. Notable people with the surname include:
Georgi Gelashvili (born 1983), Russian ice hockey goalie Iva Gelashvili, (born 2001) Georgian footballer Jaba Gelashvili (born 1993), alpine skier from Georgia Naira Gelashvili (born 1947), Georgian fiction writer, philologist, Germanist, and civil society activist Nikoloz Gelashvili (born 1985), Georgian footballer Tamaz Gelashvili (born 1978), chess grandmaster from Georgia Valery Gelashvili (born 1960), Georgian politician and businessman