The local teacher asked college students to translate into English an Urdu passage that talked about the killings of youngsters, including girls, by armed troops during recent popular unrest.
Noor Mohammad Bhat was arrested on Friday under the "Unlawful Activities Act and suspicion of intent to provoke the masses by causing riots", police superintendent Hazratbal Maqsood-ul-Zaman told AFP.
Armed rebel violence in Indian Kashmir has eased since rival India and Pakistan launched a peace process in 2004 over the disputed region.
But popular pro-independence protests since June have left more than 110 protesters and bystanders, many of them teenagers and young boys, dead.
The unrest, in which protesters hurled stones at police, sometimes drawing police fire in return, has left authorities grappling for solutions in Kashmir, where popular desire for independence remains strong.
The teacher set students at the state-run college in Srinagar questions such as: "Are the stone-pelters the real heroes" of the unrest this year?
The exam also asked students to translate into English: "Kashmir is burning again. Bullets are being pumped into the chests of even girls and women. Rulers continue in a deep slumber."
The exam paper "carried objectionable text against the establishment", said the police official, terming it "anti-India."
Another senior police officer was quoted by local media as saying police had to detain the teacher to ensure "separatist politics don't become part-and-parcel of the educational curriculum".
The teacher's arrest drew shock from his colleagues, who said Bhat was not known for having strong political views.
"Bhat is innocent," said Kashmir College Teachers' Association President Tariq Ashai.
"He is a teacher, a literary personality who keenly observes the happenings of his surroundings, so when he was asked to set the paper, he translated his observations and feelings on paper," Ashai added.
Nuclear-armed India and Pakistan each hold part of Kashmir but claim it in full. India says Kashmir, where an insurgency has been underway against New Delhi's rule for more than two decades, is an "integral part" of the country.
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