"We are not treating it as a terrorist incident," National Police spokesman Gil Kleiman said.
Security sources said Wednesday's blast appeared to be a settling of scores among criminals in the city.
The car blew up as it headed down a road in the industrial district of Ashkelon, about 20 km north of the Gaza Strip.
The driver of the vehicle died, police said. Israeli media identified him as a 30-year-old Ashkelon resident.
Israelis have been on edge in the face of vows of revenge from the Palestinian resistance group Hamas after Israeli occupation forces killed 14 of its fighters in the Gaza Strip on Tuesday.
Wednesday's explosion came seven days after a Hamas attack killed 16 people on two buses in the southern Israeli city of Beersheba.