Shakhtar came to Leipzig with a weakened squad after losing most of its overseas players following Russia's invasion of Ukraine, but the team scored from four of its five shots on goal.
Tedesco had taken over in December 2021 and helped Leipzig climb from 11th place to fourth and a place in the Champions League. He also led them to the German Cup, their first major trophy.
But the team have managed just one win from their five league games in the Bundesliga, including a 4-0 loss to Eintracht Frankfurt last week.
"After our mediocre start to the Bundesliga season with five points from five games, along with the recent defeats to Eintracht and Shakhtar, we believe that a change of management is the right course of action to turn things round quickly," club CEO Oliver Mintzlaff said in a statement.
Leipzig play Borussia Dortmund, joint top in the league with Freiburg, on Saturday, before a trip to Real Madrid next Wednesday.