About 90 machine gun rounds were fired at the object, which has not been identified. North Korea has flown drones over the border in the past.
In a statement, the South Korean military said it was "maintaining high vigilance".
The incident comes amid continuing high tension on the Korean peninsula.
On Sunday Pyongyang conducted what it said was a successful test of a medium-range ballistic missile.
That test came a week after North Korea tested what it said was a new type of rocket capable of carrying a large nuclear warhead.
The pace of North Korean missile tests has increased in recent months and experts fear it indicates progress towards Pyongyang's ultimate goal of putting a nuclear warhead on a missile that could strike the continental US.
The UN Security Council is to hold a closed-door meeting on North Korea on Tuesday evening. In a statement on Monday, it agreed to "take further significant measures including sanctions" to force North Korea to end its "highly destabilising behaviour".
The spike in tensions comes with a new president in South Korea. Moon Jae-in was sworn into office earlier this month after the previous leader, Park Geun-hye, was impeached. She is now on trial for corruption.
Mr Moon has adopted a more conciliatory stance than his predecessor, calling for more dialogue with the North.
South Korean military officials did not say whether they hit or secured the object that flew across the demilitarised zone, but similar incidents have occurred in the past.
In January 2016, South Korean border troops fired shots at a suspected drone.
In 2014, South Korean officials said they found two North Korean drones, one south of the demilitarised zone near Paju and the other on an island near the disputed inter-Korean maritime border.