The Games in Krakow start on June 21 and run until July 2, with 19 sports held as Olympic qualifiers.
The International Boxing Association (IBA) said the continental qualifier "totally contradicts" Olympic organisers' recommendation that Russian and Belarusian athletes be allowed to return to international competition.
"For this reason, the European Games 2023 can no longer remain an IOC recognised qualifier for Paris 2024 and must be annulled," it said.
The IBA was suspended by the International Olympic Committee (IOC) in 2019 over governance, finance, refereeing and ethical issues and the two have been at loggerheads ever since.
The IOC did not involve IBA in running boxing events at the subsequent Tokyo Olympics and also removed the body from the Paris qualification process.
Boxing is not on the initial programme for the 2028 Los Angeles Games, pending reforms.
The IOC sanctioned Russia and Belarus after Moscow's invasion of Ukraine in February 2022 but recommended last month that their athletes compete internationally as neutrals.
The athletes have been offered a pathway to return via Asian events and Olympic qualifiers as it is not possible for them to compete in Europe with the war ongoing.
Organisers of the European Games said last month that there would be no athletes representing Russia or Belarus.
"We will not allow this to happen regardless of the diplomatic efforts that are currently taking place," said organising committee president Marcin Nowak in a statement on March 29.
The IBA, whose president is Russian Umar Kremlev and whose biggest sponsor is Russian energy company Gazprom, last October lifted a ban on Russian and Belarusian boxers competing under their flags.
The men's and women's world championships, which usually rank as the biggest amateur boxing tournaments outside the Olympics, have not been recognised by the IOC as 2024 Olympic qualifiers.
IBA said in February that its championships must be recognised as qualifiers.
Both world championships have been boycotted by the United States and some European countries amid mounting concern about the sport's Olympic future.
