The National League South side only appointed the Hemel Hempstead boss in September.
But the club aren’t satisfied with progress and have decided to make a change.
Billericay’s form has taken a turn for the worst and the club have slipped out of title contention.
Home defeat to Chippenham on Saturday was the club’s fifth loss in six matches. It left the side in eighth place - their lowest position of the season.
Chairman Daniel Groves said: “This announcement is regrettable, however after a meeting this morning between myself, senior management and Dean it was clear there were differences between us that could not be resolved.
"It was therefore decided to part ways, whilst this is disappointing, it is the right decision for all concerned.
"We would like to thank Dean and his team for all the hard work and effort they have put into the club and wish them all very best for the future.
"We will make an announcement regarding the role of manager at the club in the coming days.”
Outgoing Brennan added: “We have always given our all to Billericay and although disappointed we would like to thank the club for the opportunities they have given Stuart, Myself and my team.
"The supporters have been exceptional and we will miss them. We want to wish the club every success in the National League South”