Schlesinger, 28, won her opening fight against Karolina Talach of Poland before going down to Martyna Trajdos of Germany.
She started the repechage competition by defeating Edwige Gwend of Italy and was awarded bronze after her next opponent, Clarisse Agbegnenou of France withdraw through injury.
Born in Israel, Schlesinger switched allegiances to represent Great Britain in 2014. She currently resides in Scotland.
Reflecting on her fourth European medal, and first for GB, Schlesinger said: “It feels good to win another medal.
"I have only had one competition this year due to injury, so it was good to have some fights and get back into things."