The 20-year-old, who has previously played for Crystal Palace, has been praised by Dons boss Neal Ardley following his departure.
"Brendan has a lot of talent, but he needs to be playing and at the moment we can't offer him that opportunity," Ardley told the club's official website.
"So we talked about it and decided it would be best for him if he was free to join another club at the earliest opportunity.
"I want to thank him on behalf of the club and we wish him every success in his future career."
Kiernan made 18 appearances for the Dons.