“We will continue to monitor the situation closely,” an airline representative told The National.
The airline is advising passengers who have bought tickets for travel to Baghdad to call the flydubai contact centre in Dubai to rebook or request a refund.
"Customers connecting to Baghdad will not be accepted for travel at their point of origin," Emirates said.
"We regret the inconvenience caused to our customers."
The advisory is for travel on August 30 and the airline also said it is "monitoring the situation closely”.
Tensions soar in Iraq
The decision to cancel flights from Dubai to Baghdad comes after supporters of cleric Moqtada Al Sadr stormed the government palace in Baghdad's Green Zone on Monday as the Shiite leader said he was quitting politics.
Tensions have soared amid an escalating political crisis that has left Iraq without a new government, prime minister or president for months.
Official working hours were suspended on Tuesday as unrest continued.
Iran closed its land borders to Iraq as flights to the country halted on Tuesday. The Kuwaiti embassy in Iraq is also urging its citizens to leave the country, Kuwait's state news agency reported late on Monday.
At least 23 people have been confirmed dead after being shot in Baghdad's Green Zone, according to the latest death toll from AFP.
Iraqi security forces said on Tuesday that four rockets landed in the fortified Green Zone, damaging residences.