Flight FZ215 was hit by "small arms fire" before landing on Monday but all passengers disembarked safely, a flydubai spokesperson told AFP.
The no-frills carrier, a sister firm of Emirates, said it was working with Iraqi authorities to investigate the incident, adding that it will continue to fly to its other destinations in Iraq.
Other UAE airlines, including Emirates, Etihad and Air Arabia, suspended their flights to Baghdad.
"Emirates has suspended its services to Baghdad until further notice due to operational reasons," the Dubai-based airline said.
The Abu Dhabi-based Etihad Airways said it had "suspended all flights to the Iraqi city with immediate effect and until further notice."
The website of Sharjah-based budget carrier Air Arabia also showed that flights to Baghdad were not available.
Baghdad airport staff confirmed there had been disruption to flights after Monday's incident.
"The plane was able to land normally but some airlines have cancelled or delayed their flights today," one airport employee said, speaking on condition of anonymity.
Flights from some of the other major airlines flying to Baghdad, such as Turkish Airlines and Royal Jordanian, were delayed, their websites showed.
"The exact timing of flights is not yet clear. Operation directors are currently having a meeting," a Turkish Airlines official told AFP in Ankara.
Western airlines flying over Iraq have taken extra precautions in recent months for fear that jihadists of the Islamic State group might acquire weapons able to hit cruising airliners.
Baghdad International Airport is located west of the capital, near the province of Anbar, which is largely controlled by IS fighters.
