The dam helps distribute water from the Euphrates river on its course through the western province of Anbar.
It is located five kilometres south of the city of Falluja, which was overrun by militants early this year.
Iraqi troops have since been surrounding Falluja and shelling the city in an effort to dislodge anti-government tribes and insurgent factions.
They include the Islamic State in Iraq and the Levant (ISIL), which in February, took control of the Nuaimiya area where the dam is located.
ISIL then began fortifying its positions with concrete blast walls and sand bags, according to anti-government tribesmen, who said no other groups were involved in the takeover.
The militants closed all eight of the dam's 10 gates one week ago, flooding land upstream and reducing water levels in Iraq's southern provinces, through which the Euphrates flows.
The anti-government tribal fighters said ISIL's tactic was to flood the area around the city to force troops to retreat and lift the siege on Falluja.