A three-paragraph statement on the Lakers' website announced Brown was "relieved" of his coaching duties.
The statement said assistant coach Bernie Bickerstaff would serve a interim head coach and a search for a new head coach would begin immediately.
"This was a difficult and painful decision to make," Kupchak said. "Mike was very hard-working and dedicated but we felt it was in the best interest of the team to make a change at this time. We appreciate Mike's efforts and contributions and wish him and his family the best of luck."
Los Angeles lost its first three games this season before beating Detroit -- in a game between winless teams. The Lakers fell to 1-4 after losing at Utah Wednesday.
Team owner Jerry Buss had given Brown a vote of confidence Wednesday.
Brown, 42, led the Lakers to a 41-25 record last season, which ended with the Lakers losing to Oklahoma City in the second round of the playoffs.
He previously coached the Cleveland Cavaliers for five seasons, building a 272-138 record. The Cavaliers advanced to the NBA Finals in 2007.