Assistant manager Keith Millen has been put in temporary charge of first team affairs whilst City seek a replacement manager.
"I am very disappointed Brian has decided to stand down," Millen told the club's official website.
"He was instrumental in my appointment as assistant manager and it's been a pleasure working with him.
"I would like to place on record my thanks to him and I'm just sorry it hasn't worked out for him at the club.
"The chairman told me he would be happy for me to apply for the post but it's too early to reply on that front."