The three men were among a group of eight detained by the army last week in Poonch, near the frontier that divides the restive Himalayan territory between India and Pakistan.
They were arrested a day after militants ambushed and killed four soldiers who were travelling to an army outpost in the district.
"The army has ordered a Court of Inquiry to investigate the circumstances which led to the deaths of three civilians," a senior police official in Kashmir told AFP on condition of anonymity.
Internet services were shut off in Poonch and neighbouring Rajouri district after the attack on Indian soldiers.
But on the weekend, footage purporting to show Indian soldiers physically abusing some of the detainees was published on social media and shared widely.
One man among those detained told the Indian Express that he had appeared in the viral video.
Mohammad Ashraf, 52, told the newspaper he and the other detainees were stripped, beaten and had their open wounds painfully smeared with chilli powder.
Three army officers had been transferred from their posts while the army probe was underway, the newspaper added.
The other five civilians detained by the military had sustained injuries and were being treated at a hospital in Rajouri.
Indian army chief General Manoj Pande visited Poonch on Monday and told commanders to conduct their operations "in the most professional manner", according to an army statement that did not mention the allegations.
Residents of Topa Pir, the site of last week's attack on soldiers, told AFP on condition of anonymity that the eight civilians taken into army custody were all from their village.
Rebel groups have waged an insurgency in the Indian-controlled portion of Kashmir since 1989, demanding independence or a merger with Pakistan.
The conflict has left tens of thousands of civilians, soldiers and militants dead.
India has more than 500,000 troops permanently stationed in Kashmir and, like Pakistan, claims the divided territory in full.
It blames Pakistan for backing the militants, a charge Islamabad denies, saying it only supports a Kashmiri struggle for the right to self-determination.
This month India's top court upheld a 2019 decision by Prime Minister Narendra Modi's government to revoke the limited autonomy of the Muslim-majority region.
That move was accompanied by mass arrests and a months-long internet and communications blackout to forestall protests.
Related Links
News From Across The Stans
| Subscribe Free To Our Daily Newsletters |
| Subscribe Free To Our Daily Newsletters |
