Senior military official Brig-Gen Abdul-Salam al-Hassi blamed the late Friday attack outside the Jalaa hospital on Islamic militants.
Mohammed al-Zawy, an official at the hospital, confirmed that five people were killed and 14 wounded in the blast. He said the explosives-laden car was parked near the hospital's outpatient entrance door.
Friday's attack was a grim reminder of the wave of car bombings and assassinations that wracked Benghazi after the nation's 2011 civil war and the chaos and bloodletting that followed. Some 200 people were killed during the violence in Benghazi in 2012 alone.
Military police cordoned off the hospital area after the blast, which sent a column of black smoke rising over the parking area.