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The front of the building and nearby houses were damaged in the attack in the upscale district of Fuwayhat.
The Swedish mission – one of the few diplomatic offices in Benghazi – was empty during the attack.
It is the latest in a series of attacks on foreign embassies as Libya struggles to deal with lawlessness since 2011.
The car bomb was detonated by remote control on Friday, according to officials.
No staff were injured in the attack as the embassy is usually closed on Fridays, says Swedish foreign ministry spokesman Ursula Ahlen.
It comes a day after Libyan Prime Minister Ali Zeidan was seized from a Tripoli hotel and briefly held by armed militiamen for undisclosed reasons.
Earlier this month, staff from the Russian embassy were evacuated after gunmen attacked its compound in Tripoli.
A car bomb was also found outside the Italian embassy in June and the UK withdrew some embassy staff in May over security concerns.
The most serious incident occurred last year, when US ambassador Christopher Stevens was killed in an attack on the US Consulate in Benghazi, alongside three other US officials.
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