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.