Soldiers reportedly brawled with sticks, bats and bamboo sticks studded with nails in the late-night confrontation in the Ladakh region on Monday.
However, no shots were fired.
India's army said that both sides suffered casualties. China confirmed the incident but did not give details.
The Indian statement notes that injured soldiers were "exposed to sub-zero temperatures in the high altitude terrain".
It is the first deadly clash between the two sides in the border area, in the disputed Kashmir region, in at least 45 years.