Initial reports claim a Hamas operative was hit in the strike.
Unconfirmed reports put the death toll at one with possible injuries to passers-by.
But there are conflicting accounts that the operative survived.
Photographs of the aftermath show the car was hit in a built-up residential area.
Following the strike, people on social media reported the presence of Israeli Defence Force (IDF) recon aircraft and helicopters in the west of the central region.
Red-alert siren alarms also sounded in southern Israel near the Gaza border.
The IDF said in a statement: “Following reports regarding sirens in the Sha’ar HaNegev Regional Council, one launch was identified from the Gaza Strip at Israeli territory.”
Palestinian local reportied the entry of IDF aircraft into Gaza airspace.
The explosion comes after another strike by IDF against two other Palestinian cars on Tuesday.
Israeli drones destroyed two cars and an observation post that were being used by Palestinians to launch incendiary balloons into southern Israel from the Gaza Strip.
The IDF confirmed that its aircraft conducted three strikes in response to repeated arson attacks from the Palestine costal enclave.
In a statement, the IDF said: “An IDF aircraft attacked a car in the northern Gaza Strip that was being used by a group of incendiary balloon launchers, as well as an observation post from which they were launching balloons.”
No injuries were reported following the initial strikes.
At around 8pm local time (6pm GMT) the air force conducted an additional airstrike also east of Gaza City.
A number of small fires were reported in southern Israel throughout the day on Tuesday.
They were apparently started by incendiary kites and balloons from Gaza.