Andrabi was involved in terror funding and other secession activities since 1987, it said.
"Andrabi started protests and raised slogans against display of pictures of women without burkha in cinema halls. Dukhtaran-e-Millat splashed black ink on pictures of women without burkha," NIA said.
Other militant groups supported her and announced through pamphlets that those who didn't obey the order would be punished with bullets, the NIA added.
By January 1990, all 15 operational cinema halls were shut in Kashmir.
Andrabi's husband Ashiq Hussain Faktoo alias Mohammed Qasim is serving life-term in J&K jail for killing H.N. Wanchoo, a Kashmiri Pandit, the agency said.
On October 4, the NIA filed a second supplementary charge-sheet in the terror funding case under the new Unlawful Activities (Prevention) Act against J&K Liberation Front (JKLF) chief Yasin Malik, founder chief of the J&K Democratic Freedom Party Shabir Shah, Asiya Andrabi, All-Party Hurriyat Conference General Secretary Masarat Alam and former legislator Rashid Engineer.
Andrabi had caught public attention in May 2015, when she criticised Bollywood superstar Salman Khan for advocating re-opening of cinemas. She had called Salman Khan an Indian agent helping cultural aggression of Kashmir by India and asserted that re-opening of cinemas would be opposed at all costs by her group.
Salman Khan had advocated re-opening of cinemas in the Valley, stating everyone watched movies on television and through pirated CDs, which could be checked with the Valley getting its cinemas back.
Andrabi was arrested on June 4 in connection with the terror funding case, which the NIA had registered in May 2017 after violence erupted in the Valley.
The agency has arrested several separatist leaders on charges of receiving funds from Pakistan to carry out terrorist activities and stone pelting in 2016.
(Ananya Bhatnagar can be contacted at ananya.b@.in and Amiya Kumar Kushwaha at amiya.k@.in)
( With inputs from IANS )