The 20-year-old winger saw his opportunities limited this season at Kingsmeadow and manager Neal Ardley has allowed him to find employment elsewhere.
"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 Dons' 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 came through the ranks at Wimbledon after leaving Crystal Palace in 2009.
The youngster made his debut as a substitute in a 3-1 defeat at Crawley in March 2011 and went on to make 18 appearances for the Dons.