Jurgen Klopp, Head of Soccer at parent company Red Bull, was not named in the statement and has said previously he would not step in as coach, whether on a permanent or interim basis.
Later on Sunday, Leipzig named Zsolt Low as Rose's replacement on an interim basis until the end of the season.
Low has previously served as an assistant coach at Leipzig, as well as Bayern Munich, Paris Saint-Germain and Chelsea.
Leipzig slipped to sixth in the table after Saturday's 1-0 loss at Borussia Moenchengladbach, their sixth successive away match without a win.
The Saxony club are three points behind a place in the top four and Champions League qualification for next season.
They face a tight battle for the remaining two spots, with league leaders Bayern Munich and defending champions Bayer Leverkusen all but assured of a place in next season's competition.
Leipzig-born Rose took over in September 2022 and guided them to a German Cup triumph in his first season in charge, along with third place in the league.
The club also won the DFL Supercup, equivalent to England's Charity Shield, with a 3-0 win over Bayern Munich at the start of the 2023/24 season.
Last season, Leipzig finished fourth, with Germany awarded five Champions League placings due to UEFA coefficient placings.
"We believed in Marco and his team for a very long time and tried everything until the very end to turn things around together," sporting director Marcel Schaefer said in a statement.
"However, given the current situation and the lack of results, we are firmly convinced that we need a new impetus for the remaining games to achieve our goals this season."
Leipzig thanked Rose for his time at the club, but the coach was not quoted in the statement. The remainder of his team were also dismissed.
The 48-year-old, who previously coached Red Bull Salzburg, Borussia Monchengladbach, and Borussia Dortmund, was under contract until June 2026.
Besides their stuttering league form, Leipzig lost seven of eight games in this season's Champions League and failed to qualify for the knockout stages.
The two-time German Cup winners travel to Stuttgart to play in the semi-finals of the competition on Wednesday.
Leipzig, owned by Red Bull since 2009, have only missed out on the Champions League once since the 2016/17 campaign in the Bundesliga and made it to the semi-finals of the competition in 2020.