"The strike is to protest this gross human rights violation," said chief organiser Syed Ali Geelani in a statement.
The strike was widely followed in the main city of Srinagar and other towns, including Sopore where the weekend incident happened, police sources and residents said.
Nazim Rashid, a shopkeeper, was detained by counter-insurgency police on Saturday in the northern town of Sopore. He was declared dead early Sunday, with no reason provided as to the cause.
Police said Monday they had registered a murder case and suspended three officers following the death of the 28-year-old man.
But Geelani insisted there should be an impartial enquiry by a UN body or international human rights groups.
Kashmir Chief Minister Omar Abdullah promised "swift and exemplary action" in a Twitter post on Sunday.
Rashid's family has also called for an independent probe, even as the Sopore police chief was transferred late Tuesday to ensure a "free and fair probe".
Last year more than 110 people were killed when police and security forces opened fire during a series of demonstrations triggered by the death of a 17-year-old youth who was hit by a police teargas shell.
Last week there were protests against the alleged rape of a woman by soldiers.
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