Zhang Shuili, deputy director of the western theatre combat bureau, said the incident took place in "recent days". He did not give an exact location.
He said that India had "violated China's territorial sovereignty".
The two countries saw relations worsen this summer when they became locked in a dispute over a Himalayan plateau.
India has yet to respond to China's latest claim.
In remarks carried widely by state media outlets, Mr Zhang said Chinese border forces had conducted "verifications" of the alleged drone.
He added that China expresses "our strong dissatisfaction and opposition regarding this matter" and that it would "steadfastly protect the country's rights and safety".
Relations between the two countries soured in June when India said it opposed a Chinese attempt to extend a road on the Doklam/Donglang plateau at the border of China, India and Bhutan, reports BBC.
The stand-off ended in August when both countries pulled back their troops.