According to the Turkish Boxing Federation website, athlete Serhat Güler and trainer Seyfullah Dumlupınar contracted the virus at the European qualifiying tournament.
"While the world was taking extreme measures to deal with the virus, I am baffled that an IOC taskforce and the British government allowed the tournament to start even though many of us had concerns and almost every other sport had shut down," federation President Eyup Gozgec was quoted as saying in the Guardian.
London's Copper Box arena hosted the official Olympic qualifying tournament, featuring boxers from 40 nations.
It continued for three days despite virtually every other sport being suspended because of the pandemic.
In a letter to other boxing federations, seen by the Guardian, Gozgec, who is also vice-president of the European Boxing Confederation, said: "Unfortunately, two of our athletes and our Turkish head coach have tested positive for the new type Covid-19 coronavirus after returning to Turkey from London.
"All of them are in treatment now and thankfully they are in good condition. This is the disastrous result of the irresponsibility of the IOC taskforce.
"This virus has been around since December 2019. Therefore, it is inevitable to ask why the European qualification event was not postponed before it took place?
"They did not consider anyone's health, which led them to organise this horrible event." (Reporting by Martyn Herman, editing by Ed Osmond)