The blast at Sabiha Gokcen, the city's second airport and located on its Asian side, occurred shortly after 2:00 a.m. (midnight GMT), local budget carrier Pegasus said, fatally wounding a cleaner on one of its planes.
The airport's owner, Malaysia Airports, referred to more than one explosion "at the tarmac area", adding that normal flight operations had resumed by 0200 GMT.
Police declined comment, while the airport said investigations into the cause of the blast were ongoing.
Bomb attacks by Kurdish, leftist and Islamist militants are common in Turkey. A three-decades-old conflict between the state and the militant Kurdistan Workers Party (PKK) has flared up in the country's mainly Kurdish southeast since the collapse of a ceasefire in July.
No passengers were in the area at the time of the airport blast, which the Dogan news agency caused damage to at least three planes as far as 300 meters (330 yards) from each other.
A photo on Dogan's website showed a hole in one plane window. Video footage showed investigators taking photos of a terminal building wall, dozens of meters from the nearest planes.
Police armed with rifles and protective vests imposed tight security at entrances to the airport, searching vehicles while a police helicopter circled overhead, state-run Anadolu Agency said.
According to its website, Sabiha Gokcen served around 26 million passengers in the first 11 months of the year, less than half the number at the main Ataturk airport on the European side of the city.