With Brown's departure, the franchise will be searching for a general manager for the ninth time since it returned to Cleveland in 1999.
Winless thus far this season, the Browns own a 1-27 mark under the watch of Brown, who was hired to run the front office on Jan. 3, 2016.
"We have great appreciation and gratitude for Sashi's commitment and leadership to our organization but believe transitioning to someone with strong experience and success in drafting and building consistently winning football teams is critical to the future of the Cleveland Browns," Browns owner Jimmy Haslam said in a statement. "Today we informed Sashi that we were going in a new direction.
"The 2018 draft and offseason is pivotal for our franchise, we need to ensure that we maximize our opportunity for success; with our picks, free agency and building our roster.
"Hue Jackson will remain our coach and will return for the 2018 season but we feel it is necessary to take significant steps to strengthen our personnel department. We have begun the process of having productive conversations regarding leadership of our football operations and will provide further updates when appropriate. We thank Sashi for all his hard work and dedication to the Cleveland Browns."
Brown's regime has been marked with strikeouts at the quarterback position, namely trading out of the No. 2 spot in the 2016 NFL draft as Philadelphia moved up to select Carson Wentz. Wentz has an NFL-leading 29 touchdown passes this season.
The Browns have stockpiled picks for future drafts, with six additional picks in April's draft.