Officers from Belgium and France searched houses in the country, leading to the arrests - 13 in each country.
Twenty-one migrants were found during inquiries on May 26 and subsequently taken to safety.
Three vehicles, cash and electronics were also seized during the searches, which focused on properties in Brussels and Paris.
The organisation is suspected of transporting mainly Vietnamese immigrants through Belgium and France towards the UK.
The victims are thought to have been hidden by the suspects before being taken on their final leg of their journey.
Europol set up an operational task force in order to ease the transfer of information between the law enforcement agencies investigating the Essex lorry deaths, this group aided with the latest arrests made on the continent.