A magistrate speaking to AFP on condition of anonymity said at least 4,000 people were arrested and held under the Public Safety Act (PSA), a controversial law that allows authorities to imprison someone for up to two years without charge or trial.
"Most of them were flown out of Kashmir because prisons here have run out of capacity," the magistrate said.
He used a satellite phone allocated to him to collate the figures from colleagues across the Himalayan territory amid a communications blackout and lockdown imposed by authorities.
Authorities have repeatedly declined to provide a tally of how many people have been taken into custody.
They only confirmed that more than 100 local politicians, activists and academics were detained in the first few days after the state was stripped of its semi-autonomous status.
They said the "few preventive detentions" were made to avoid a "breach of the peace" in a region that has fought an armed rebellion against Indian rule for three decades.
Those detained include high-profile former chief ministers Mehbooba Mufti and Omar Abdullah.
Jammu and Kashmir government spokesman Rohit Kansal said previously there was "no centralised figure" for the total number of people detained.
But AFP spoke to numerous government officials in Kashmir's main city of Srinagar, including police and security personnel, who confirmed the sweeping arrests.
A police official who asked to remain anonymous told AFP "around 6,000 people were medically examined at a couple of places in Srinagar after they were detained".
"They are first sent to the central jail in Srinagar and later flown out of here in military aircraft," he added.
Residents living around the airport in Srinagar, where the Indian Air Force controls air traffic, say military aircraft land and take off every night.
Another security official said "thousands are jailed" but that the figure did not include other residents whose detentions at police stations had not been recorded.
Families of those detained were reluctant to speak to AFP, fearing they would get into trouble with authorities.
A resident who asked not to be named told AFP a shopkeeper was arrested despite not taking part in protests, with a police officer telling him he was detained "because he talks a lot".
Authorities on Sunday earlier reinstated the heavy restrictions even though they had earlier said they would ease them, after eight people were injured during protests.
They have previously denied or played down reports of any violence and stressed that most of the Muslim-majority Kashmir Valley has been peaceful.
A senior government official told AFP earlier Sunday that more telephone exchanges would return to normal operations "by the evening" and schools in some areas would reopen on Monday.