Firefighters recovered 11 bodies from the vehicle, which had been travelling towards Thessaloniki.
The driver of the truck, which had been heading towards the town of Kavala, escaped the unscathed.
“The people are charred and hard to identify,” a traffic police officer told DPA.
Three minors were among those killed in the fiery crash, the cause of which was not initially clear.
Greek police said the car involved in the crash had been used for migrant smuggling in the past.
It had failed to stop earlier in the day when police officers tried to pull it over for a check.
Last June, a migrant smuggling van carrying 16 people, mainly from Syria and Iran, crashed near Kavala, killing six people including three children.
“We are deeply saddened by the devastating news from an area where thousands of refugees have risked their lives and crossed into Greece on irregular routes,” said Philippe Leclerc, the United Nations High Commissioner for Refugees (UNHCR) representative in Greece, in a statement.
At least 40 deaths have been recorded in the region in 2018, nearly half having drowned in the fast-flowing Evros River.
“These horrific deaths are part of the broader dangers faced by people who find themselves at the mercy of human smugglers, who exploit their vulnerability”, the UNCHR statement added, calling for “alternatives to these dangerous crossings for people in need of international protection”.
Greece reports near daily arrests of smugglers carrying migrants from the Turkish border.
More than 12,700 refugees and migrants have crossed into Greece’s northeast since the start of the year, according to data compiled by the UNHCR, more than double the number in 2017.
However, it is difficult for migrants who want to reach Central and Western Europe by way of Greece, as the so-called Balkan Route north through Albania, Montenegro and Bosnia-Herzegovina has largely been closed off and the borders fortified.
