Al Jazeera's Imran Khan, reporting from Baghdad, said ISIL suicide bombers detonated eight fortified car bombs near the army's headquarters on Sunday.
The correspondent said the group had mounted an attack on missile batteries first and then moved toward the bases.
He said ISIL had been "learning to exploit" the Iraqi military's weaknesses.
"They're using these car bombs to devastating effect. These car bombs are very difficult for the Iraqi security forces to defend against."
Fallujah is less than 70km west of Baghdad.