The car blew up outside the Tibesti hotel in a square popular as a gathering place for demonstrations in support of Libya's army.
There were no demonstrations planned, AFP reported.
The oil-rich North African nation has been in turmoil since an uprising toppled longtime leader Moamer Kadhafi three years ago, with interim authorities facing powerful militias that fought to oust him.
Benghazi was the cradle of the uprising, and is regularly the scene not only of fighting but also the murders of members of the security forces, political activists and journalists.
At least 17 people have been killed this week in fighting for control of the airport, the last redoubt of forces loyal to a former general who launched a campaign against the militants in May.