Born in Germany, Ioannidis moved to Greece at a young age and passed through the academy of Olympiacos. After making his Olympiacos debut at age 19, Ioannidis would gain experience in Europe in a series of loans to Hansa Rostock, PEC Zwolle, and Borussia Dortmund II. Thereafter, Ioannidis would leave Olympiacos, and he has since played in Super League 1 for Asteras Tripolis, Apollon Smyrnis, and Ionikos before joining Athens Kallithea FC in January 2023.