The bomb exploded a day after Libya's Prime Minister Ali Zeidan was briefly abducted by a group of former rebels.
Nobody claimed responsibility for attack, which took place days after a U.S. special forces' raid captured a Libyan al Qaeda suspect in Tripoli, outraging the Libyan opposition groups, who called for revenge attacks.
The Swedish Foreign Ministry said none of its staff had been injured. "The facade and windows were damaged but no staff was injured. The consulate is closed on Fridays," Foreign Ministry spokeswoman Ursula Ahlen said.
Libya is deep in turmoil two years after the fall of Muammar Gaddafi, with its central government and army struggling to control rival militias who have turned the vast North African country into a safe haven.
On Thursday, former rebels now on government payroll kidnapped Zeidan from the hotel where he stays in the capital Tripoli, saying the government has been informed in advance of the U.S. raid.
They later released him unharmed after a few hours. Zeidan, who is under pressure from rival militias and ordinary Libyans for failing to deliver on public services since Gaddafi's overthrow, avoided any criticism of his captors.
To help maintain security, Libya's government relies on militias made up of thousands of Libyans who took up arms against Gaddafi. But these rival groups have often involved into security threats themselves.
This is especially true for Benghazi, where the 2011 revolt began and where the U.S. ambassador was killed during an assault on a U.S. diplomatic mission a year ago.
NJF/NJF