The police in Morahalom, Hungary, said that they had taken the driver from Serbia. He was one of four victims in the accident.
Hungary is located on one of the major migrant transit routes to the EU via the Balkans or Eastern Europe.
Initial information did not include details about the nationalities or ages of the victims.
Photographs of the accident showed a car with Serbian license plates in front the flower shop's damaged wall. The building sustained no injuries.
Just before midnight Monday, there was another crash involving illegal immigrants trying to cross into Europe.
Austrian police stopped a bus carrying 30 people that crossed from Hungary to Austria in October. The driver fled after the police found two bodies inside.
It is well-known that the smuggling route to Central Europe can be dangerous for those who make it.
In August 2015, the most horrific case of its kind occurred in Austria. 71 people were killed in Iraq, Syria and Iran, while large numbers of migrants and refugees were crossing the Balkans to the EU.
The victims died from their injuries in a small meat truck that was traveling along the Hungarian-Serbian border. A Hungarian court sentenced four people to 25 years imprisonment.
Since the 2015 and 2016 influx, Hungary has tightened its asylum rules. In November, the EU's highest court ruled that Hungary had not fulfilled its obligations under EU law and refused to accept asylum applications from anyone arriving from a safe third country.