The 29-year-old will stay with the Athens outfit until the end of the season, taking him up to the conclusion of his current Blues deal.
Clark told bcfc.com: "Darren is a talented footballer but for whatever reason since he’s come to Birmingham it hasn't happened for him. He’s found it more and more difficult.
"Maybe he has lost a bit of confidence. I think the fresh start for him and his family will prove to be productive. As a club and as me as the manager I wish him well."
Having joined from Crystal Palace in the summer of 2012, the ex-Ipswich Town, Newcastle United and Charlton Athletic man made ten first-team appearances for Blues, scoring once.
Apollon are managed by former Northern Ireland manager Lawrie Sanchez and currently sit 12th in Greece's 18-club top tier.