The 30-day halt is the first of its kind in the held valley for nearly two decades, and follows an escalation of violence in recent months in the Muslim-majority Himalayan region.
India has 500,000 troops in Kashmir, which is divided between India and Pakistan and claimed by both.
Home Minister Rajnath Singh said the suspension was to allow a peaceful celebration of the fasting month.
The decision means Indian troops will stop door-to-door house searches but they will still retaliate if attacked, officials said.
In a statement, Singh sought the cooperation of “everyone” in the initiative but did not make a direct call to suspend hostilities.
There was no immediate response from freedom fighters that have been fighting Indian occupation in the territory for nearly three decades.
Indian authorities and Hizbul Mujahideen both briefly stopped fighting back in 2000.
However, the conflict has never shown any serious sign of ending.
Violence escalated after Indian troops killed Burhan Wani in a 2016 gunfight that led to months of street protests in which scores of demonstrators were killed.
Dozens of young men have since joined the freedom movement and there are now almost daily gunfights between them and Indian soldiers.
More than 200 freedom fighters and 57 civilians were killed in 2017. Many of the civilians were killed in protests to stop troops firing on holed-up fighters.
More than 70 fighters have been killed this year in dozens of gunfights and more than 30 civilians have also died.
Chief Minister Mehbooba Mufti, who runs the government in Indian held Kashmir in an alliance with Prime Minister Narendra Modi’s Bharatiya Janata Party, expressed hope that the decision “will create a peaceful and amicable environment for sustained dialogue”.