Security forces will, however, retain the right to retaliate if attacked or to protect civilian lives, Mr Singh added.
The Home Minister's surprise announcement made on Twitter comes days after Chief Minister Mehbooba Mufti pitched for the ceasefire, or a cessation of anti-terror operations, following an All Party meeting.
But Ms Mufti was badgered by the state's BJP unit which told the centre to spike her recommendation, arguing that "we should not do anything to demoralise the security forces". Union minister Jitendra Singh had suggested that leaders advocating the ceasefire were "playing politics".
The government and the Union Cabinet, which backed the centre's initiative at its meeting today, did not seem to agree.
In a series of tweets after the cabinet meeting, Home Minister Rajnath Singh said the government expects everyone to cooperate in this initiative and "help the Muslim brothers and sisters to observe Ramzan peacefully and without any difficulties".
"Decision taken to help the peace loving Muslims observe Ramzan in a peaceful environment... It is important to isolate the forces that bring a bad name to Islam by resorting to mindless violence and terror," Mr Singh said.
It is not clear how the centre's cessation of hostilities order will work on the ground. For now, army sources told NDTV that they could conduct operations "if there is specific intelligence against terrorists".
Mr Mufti welcomed the ceasefire and thanked Prime Minister Narendra Modi and Home Minister Rajnath Singh "for their personal intervention". She also expressed her gratitude to leaders and parties who participated in the All Party meeting and, according to her, "helped build consensus towards this announcement".
As a concept, sources had earlier told NDTV, the ceasefire was an idea that the Prime Minister's Office had been looking at for some time in line with PM Narendra Modi's promise from Red Fort last August that the state's problems could not end solved by bullets or abuses but embracing Kashmiris.
PM Narendra Modi is visiting the state on May 19.
But the perception in Jammu and Kashmir had been that the government had not taken any concrete steps in line with the sentiments expressed by PM Modi but continued with, what has been described as, the government's muscular approach.
Ideally, the centre would have liked that the demand for a ceasefire came from Kashmiri separatists rather than be seen as the first mover.
The security establishment does have misgivings about stopping operations. Defence Minister Nirmala Sitharaman hinted her reservations during visit to Jammu this week when she was asked about Ms Mufti's proposal. "The army's position is that it has to be firm on terrorism," she said.