Defence ministry official in Benghazi Saleh al-Bargathi said nine people died, including two children. However, other sources spoke of three deaths.
The blast follows a string of bombings in the eastern city in recent days.
Security remains precarious in Libya since the uprising against long-time leader Muammar Gaddafi, with protests by militias and attacks by Islamists.
‘Totally destroyed’
Mr Bargathi told the BBC that nine people had been killed and another 17 wounded in the Benghazi blast.
Explosives were placed in a grey Toyota car, he said.
However, in Tripoli, Interior Minister Ashour Shwayel told a Libyan TV channel that the number of fatalities was two or three.
The explosion happened in the Jalaa hospital car park, according to AFP news agency.
It quoted Libyan Deputy Interior Minister Abdullah Massoud as saying that the bomb had “totally destroyed a restaurant and seriously damaged nearby buildings”.
So far no group has claimed responsibility for Monday’s attack in Benghazi, which is regarded as the cradle of the revolution that ousted Gaddafi in 2011.
Angry crowds later gathered at the scene, blaming militants for the bombing and urging the authorities to drive them out of the city.
Many demonstrators chanted “Rise, Benghazi!”
“This is the flesh of our sons, this is what the militias have given us,” one of the protesters was quoted as saying by Reuters. “All we need here are the police and the army.”
This is the latest in a string of attacks across the country in recent months:
$1· At least three police stations were bombed in Benghazi last week – causing damage but not casualties
$1· In April, a car bomb exploded outside the French embassy in the capital, Tripoli, wounding two French guards and several residents
$1· In September 2012, the US consulate in Benghazi was attacked by armed men, leading to the killing of ambassador Christopher Stevens and three other American officials
Earlier this month, the UK said it had withdrawn some of its embassy staff in Libya in response to what London described as “ongoing political uncertainty”.