The car blew up just metres away from the rebel movement's headquarters and near a square where supporters of the uprising that began in mid-February often gather. The incident rattled nerves among residents fearing a collapse in law and order as the Libyan conflict drags on.
Ten people were injured, with seven of those suffering minor injuries, the rebel interim national council spokesman Abdel Hafiz Ghoga said.
Ghoga said the owner of the car had dynamite in the vehicle with a fuse attached to it, which exploded accidentally.
"The owner of the car came forward and regretted the incident, he said it was his car and that it was not carried out purposefully," Ghoga told a news conference.
"This was an accident." An investigation was continuing.
Loud blasts and sustained gunfire are common in Benghazi and usually blamed on anti-Gaddafi celebrations or family feuds, but car bombs are rare.
Explosives are easily accessible in eastern Libya, where protesters raided arms depots left behind by Gaddafi forces after the uprising began.
The rebel administration says it is working to boost security in the region, and has urged Libyans to return weapons taken from arms depots and police stations.