Maliki's remarks came a day after a disastrous military operation against militants in Anbar province, west of Baghdad, where the protest site is located, in which five senior officers and 10 other soldiers were killed.
If security forces move against the site, where Sunni Arab demonstrators have gathered near the city of Ramadi for almost a year, it would likely inflame widespread discontent among the minority community and could lead to an increase in the already-rampant violence plaguing the country.
"We now have a headquarters for Al-Qaeda leading the armed operations against Iraq and the Iraqi people, and this is something about which we cannot be silent," he said.
Maliki called on "those who are with them in this place who refuse sabotage and who have legal or illegal demands ... to leave these camps, and leave this place, so that Al-Qaeda stays alone," adding that protesters had a "very short period" in which to leave.
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Demonstrations broke out in Sunni-majority areas of Iraq at the end of last year, after security forces arrested guards of then-finance minister Rafa al-Essawi, an influential Sunni Arab politician, on terrorism charges.
The arrests were seen by Iraqi Sunnis as the latest example of the Shiite-led government targeting one of their leaders, but the demonstrations were about far more than just Essawi.
Anger among members of Iraq's Sunni Arab community, who say they are both marginalised by the Shiite-led government and unfairly targeted with heavy-handed tactics by security forces, has driven the demonstrations to continue.
The last major security operation at a protest site, which took place near the northern town of Hawijah on April 23, sparked clashes in which dozens of people were killed.
Shortly thereafter, the nationwide death toll from violence spiked, reaching a level not seen since 2008, when the country was just emerging from a brutal period of sectarian killings.
The violence, which was been further exacerbated by the civil war in neighbouring Syria, has killed more than 6,600 people since the beginning of 2013, according to AFP figures.