The minister said that the attacker first opened fire with Kalashnikov rifle and then blew himself up.
The explosions occurred at the airport's international terminal, according to initial reports.
A witness told CNN Turk that gunfire was heard from the car park at the airport.
Turkish officials suspect that the blast may been suicide attack.
A number of ambulances were also deployed to the scene.
Meanwhile, Turkish Prime Minister Binali Yildirim ordered the formation of a crisis desk into the incident.
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