The United Nations' Special Rapporteur on Human Rights Defenders, Mary Lawlor, said she was disturbed to hear about Mr Parvez's arrest. "He is not a terrorist, he is a human rights defender," she wrote on Twitter.
The arrest also comes at a time when tensions are boiling over in the Kashmir valley after the recent death of two civilians.
Police said the men were allegedly killed in crossfire when security forces attacked suspected militants in Srinagar. But families of the civilians have denied the police version of events, saying they were deliberately killed by Indian troops while being used as a human shield.
The deaths sparked days of protests in the region, which has seen an insurgency against Indian rule since 1989.
Both India and Pakistan claim the territory in its entirety but control only parts of the region. The nuclear-armed neighbours have gone to war twice over it.
For years, India has accused Pakistan of pushing thousands of militants across the border to foment instability in Indian-administered Kashmir. Islamabad denies the charge.