The German side were defeated 4-1 by Shakhtar Donetsk in front of their own fans on Tuesday night in Group F.
It follows a poor start to the season with just one win from the opening five league games, leaving them 11th in the Bundesliga.
Also leaving the club is former Celtic full-back Andreas Hinkel.
Italian-born Tedesco took over Leipzig in December 2021 having previously been in charge of Spartak Moscow and Schalke 04. He guided the team to a fourth-place finish and into the Europa League semi-finals where they were defeated by Rangers.
The club tweeted: “RB Leipzig have parted company with Domenico Tedesco with immediate effect. Assistant coaches Andreas Hinkel and Max Urwantschky have also left the club. RB Leipzig will announce his successor in due course.”
Celtic face on October 5 in Germany.
Thomas Tuchel could be an option as new manager having left Chelsea.