The shelling follows days of low intensity fighting, with soldiers continuing to push further into the camp.
Almost all of the camp's 31,000 residents have been evacuated.
Fatah al-Islam has also recently fired two Katyusha rockets on nearby villages, killing a Lebanese teenager and injuring a young girl.
Throughout last week, the army used loudspeakers to urge the fighters to surrender or allow their families to leave the camp.
But, around 20 women and 45 children have stayed back.
Abu Salim Taha, a spokesman for the group, has also warned they would send suicide bombers against the army if it continued its offensive.