The 30-year-old joined the League One side from Carlisle United last summer.
Kiwomya has revealed that finances played a part in the decision to allow Zoko to leave Meadow Lane.
"He's one of the highest earners. I've got restraints on me, and I'm trying to keep the age of the team down," Kiwomya told BBC Radio Nottingham.
"Also, he's not been playing lots of football, so it made sense.
"Both parties are happy. I'd like to thank him for his contribution to the club."
Zoko played 45 games for Notts last season.