Myanmar has experienced mass protests and a brutal military response since the 1 February coup that ousted Aung San Suu Kyi.
UN Human Rights chief Michelle Bachelet told the council on Tuesday that the situation in the country had "evolved from a political crisis to a multi-dimensional human rights catastrophe".
"Suffering and violence throughout the country are devastating prospects for sustainable development, and raise the possibility of state failure or a broader civil war," she warned.
Since the coup, nearly 900 people have been killed, while about 200,000 have been forced to flee their homes, according to UN numbers.
At the same time, at least 5,200 people had been arbitrarily arrested, including more than 90 journalists.
Andrews accused the military authorities of torture, "including torturing people in custody to death."
Some of the acts, he said, "amount to crimes against humanity", lamenting the fact that more had not been done to rein in the violations.
"The international community is failing the people of Myanmar."
'Rein of terror'
Andrews said the military had cut off food, water and medicine to those displaced by its attacks on villages.
It had "taken family members hostage when its forces are unable to find those with outstanding arrest warrants," recently arresting a four-year-old child, he said.
But the international community so far had failed to take the actions needed to bring the violations to a halt, he said.
The people of Myanmar "desperately need the support of the international community before it is too late".
"Some in Myanmar have lost hope that help from the international community will be forthcoming and have instead sought to defend themselves through the formation of defence forces and acts of sabotage," he added.
"This trend could escalate quickly and the junta's pattern of the use of grossly disproportionate force in response will likely lead to an even greater loss of life."
'Cut off their income'
"Cut off their income, and you cut off their capacity to continue their relentless attack on the people of Myanmar," he said.
The international community should also ban arms sales to the Myanmar military, launch investigations into alleged violations and work to prosecute perpetrators using universal jurisdiction laws.
There also needed to be a dramatic hike in humanitarian aid to the people through "non-junta channels", he said.
Andrews also urged countries to jointly deny the junta any claims to legitimacy it might try to make, including "the false claim that they are recognised by the United Nations".
"There is no guarantee that this approach will succeed," he acknowledged.
But "there is overwhelming evidence that the current path leads to even greater impunity, a humanitarian disaster, and a failed state."