The cause of the explosion on Tuesday, which completed destroyed the vehicle, has not been established as yet, Aljazeera says.
In a telephone call to AFP in Gaza City, the armed wing of Hamas said one of its members, Hamza Marhb, was killed in the blast.
Israel's military has flatly denied any involvement in the incident, which Aljazeera reports took place about 200 metres from the residence of the Palestinian president, Mahmoud Abbas.
Marhb, a local leader in the Ezzedine al-Qassam Brigades for the southern Gaza town of Khan Yunis, was alone in the vehicle, the faction said.
Ezzedine al-Qassam insisted that Marhb was assassinated in an Israeli air strike and denied there were any explosives in the car, which blew up as it was travelling in the Tal Hawa area of southern Gaza City.
"Israel completely denies having anything to do with the explosion in Gaza," Captain Noa Meir, an Israeli military spokesman, told AFP.
Medical sources said five civilian bystanders were wounded in the blast.
An AFP correspondent on the ground said the explosion had gouged a massive hole in the road and blown out windows of neighbouring houses and of vehicles parked in the area.
In other news, a Palestinian armed faction leader on Tuesday said a captured Israeli soldier was being held in a "secure place", and he claimed that his group also seized a Jewish settler in the West Bank.
The new claims about captive Israelis came from the Popular Resistance Committees, a violent group with close ties to the Hamas-led Palestinian government.
The PRC was one of three groups that took part in Sunday's cross-border infiltration near Gaza in which fighters killed two Israeli soldiers and abducted Corporal Gilad Shalit.
Sunday's cross-border oeration
has been claimed by the PRC
"The soldier is in a secure place that the Zionists cannot reach," PRC spokesman Mohammed Abdel Al said. It was the first acknowledgment by fighters that Shalit was still alive.
The kidnappers have not said where the 19-year-old soldier is being held or released any photos of him. Israeli officials believe Shalit sustained light wounds to his stomach and is being held in southern Gaza.
Abdel Al also said his group had taken a Jewish settler in the West Bank hostage. Israel Radio reported the settler had been hitch-hiking on Monday night and failed to return home.
"We're looking into reports of a missing person," police spokesman Micky Rosenfeld said.
Abdel Al said the release of more information would depend on Israel. "The Zionists are looking for any information. We remind them there is nothing for free," he said in Gaza.
On Tuesday, a spokesman for the military wing of the Nasir Salahudin Brigades, Abu Abeer, said one its teams had managed to snatch an Israeli settler in the West Bank last Sunday.
Speaking to Aljazeera, Abu Abeer also said the continuing Israeli threats deserve more abductions of Israeli soldiers and settlers in the context of what he called the "knights' wrath" battle.