The soldiers applied a burning stick to the genitals of one of the unarmed detainees and threatened another with a knife as they interrogated them over the location of a weapons cache, according to the video.
"Based on our preliminary report, we found that soldiers on the ground overreacted in handling those people who had been arrested," Security Affairs Minister Djoko Suyanto told reporters.
"What they did was unprofessional."
The graphic video drew international media attention to allegations of widespread torture and abuse of activists and civilians in restive Indonesian regions such as Papua and the Maluku islands.
Rights groups including Amnesty International have demanded Indonesia investigate and punish the unidentified soldiers in the video, citing an entrenched culture of impunity in the country's security forces.
Suyanto said the troops involved in the incident, which reportedly occurred in May in the Punjak Jaya region of eastern Papua province, would be dealt with "according to military regulations".
"It has attracted public and world attention. We'll settle it properly," he said.