Nembidis was born on March 10, 1928. He played for local club AC Pangrati before transferring in 1949 to Panathinaikos as a centre-forward. At Panathinaikos, he was established as a midfield-partner for Yiannis Papantoniou. He played for PAO throughout the 1950s, retiring in 1962.
Nembidis was capped 7 times by the Greek National Football Team, scoring 2 goals, both in his debut in a friendly against Syria.