The shrine has been the target of Sunni insurgent attacks before
An airport in the Iraqi city of Najaf has been closed for a week after a threat of an attack on a Shia shrine have emerged.
Reports were circulating about an insurgent group planning to hijack a plane and fly it into the Imam Ali shrine in Najaf.
Two men have been arrested in connection with information authorities received about the potential attack.
The Imam Ali shrine is one of the most revered sites in Shia Islam.
Both airports in Najaf and Baghdad were closed last week. Baghdad was reopened soon after, but Najaf stayed closed.
Officials had initially blamed the closure on radar malfunctions.
Flight paths near Najaf and Karbala, another site of Shia pilgrimage, have been diverted.
Iraqi Defence Minister Abdul-Qader al-Obeidi said the details of the plot were unclear.
"At the same time we can't neglect them," he told reporters in Baghdad.
One of the two men arrested was alleged to be the intended pilot of the hijacked plane, the other a member of the airport ground crew.
Al-Qaeda in Iraq have claimed responsibility for recent bombing attacks in Baghdad.
The targeting of Shia holy sites has been a tactic of Sunni insurgents.
A huge attack on a shrine at Samarra, north of Baghdad, following elections in 2005 sparked two years of bloody sectarian violence, the BBC's Jim Muir in Baghdad says.
Imam Ali, the cousin of the Prophet Muhammad, revered by Shia Muslims, is buried at the site of the Najaf shrine.
It was the scene of heavy fighting in 2004 between US forces and the Shia Mehdi Army, loyal to radical cleric Moqtada Sadr.