Ashraf al-Saiti, a senior medical official at al-Jala hospital, says the shelling took place late yesterday when the family's home in al-Salam district came under intense shelling from the nearby al-Sabri neighbourhood, a stronghold of Islamic extremists.
He says the children were between five and 10 years old.
Fighting has been raging in Benghazi for nearly a year, mostly between army units and fighters loyal to the internationally-recognized government on one side, and Islamic extremists, including militants from an Islamic State affiliate, on the other.