Brown took charge virtually a year ago to the day, helping the Blues to play-off contention when the season was curtailed.
He said: “Like many, the current situation has made me reflect on my current commitments and although I really enjoyed managing Clitheroe FC last season, I've made the decision not to continue.
“I’ve met some great people in my short time at the club. The chairman, committee, volunteers and supporters all made me feel welcome from the onset. The support I received was excellent and I can't thank everyone enough. Take care and stay safe.”
Brown was previously with Lancaster City, helping them to the league title in 2016/17 and the Presidents Cup.
Clitheroe chairman Lee Sharples said: “The Board of Directors wish to thank Phil and his assistant Dave McCann for all their hard work during the 2019/20 season and for their professional approach on and off the field. Phil did an amazing job during his spell with the Blues and has seen a transformation in fortunes, where he took a club that finished 18th in the 2018/29 season to finishing 6th in the 2019/20 season.
“I would personally like to thank Phil, who has been a pleasure to work with since the moment he accepted the role. Phil has always been open and honest, and always kept a clear, open line of communication with myself. I wish Phil all the best for his future whether that is at another club or whether this club was his last.
“The search for a new manager begins straight away and we will be putting out a formal advert in the next few days.”