Agencies quoting Palestinian security sources said the injured official was Yasser Dahlan, a cousin of Fatah's Gaza unit leader Mohammed Dahlan.
Also wounded was Yasser Dahlan's mother-in-law, who was in the vehicle, and a security guard standing near the stationary vehicle when the blast occured.
A local Fatah spokesman said it appeared that an explosive device had been planted in the car.
The cause of the blast was unclear and no Palestinian group claimed responsibility.
The Israeli military, which earlier on Wednesday carried out a botched air strike on alleged Palestinian fighters elsewhere in the strip, said it was not involved in the latest incident.
Mohammed Dahlan is one of the most powerful Fatah figures in the Gaza Strip but has no official position since the Islamic resistance movement, Hamas, took over the government after ousting Fatah in parliamentary elections in January.
In recent weeks Fatah-Hamas rivalry has turned increasingly violent, with activists from each side killed in gunfights and several civilians slain in the crossfire.
In one attack, rocket-propelled grenades were fired at a Rafah office of the pro-Fatah security service, by what were believed to be Hamas fighters.