Researchers from both groups travelled to the region and reported government planes dropping bombs in populated areas.
"No evident military targets were visible near any of the air strike locations," they wrote.
The bombing has reportedly wounded dozens of people, including a number of women and children.
More than 150,000 people have fled their homes since June, with many hiding in caves, abandoned homes and other makeshift shelters.
Khartoum has been fighting armed groups for months in South Kordofan, the state which includes the Nuba Mountains region.
Sudanese officials insist that their bombing raids have only targeted rebels.
Daffa-Alla Elhaj Ali Osman, the Sudanese ambassador at the United Nations, told Al Jazeera last month that rebels were responsible for civilian casualties.
But the report from Amnesty and HRW notes that many of the bombs used are unguided - in some cases, simply rolled out of cargo planes - and cannot be directed at military targets.
"Use of weapons in a civilian area that cannot accurately be directed at a military objective makes such strikes inherently indiscriminate, in violation of international humanitarian law," the groups said in their report.
Hunger a growing problem
The Sudanese government has blocked international aid agencies from entering South Kordofan, and insists that all aid to the region be delivered through the Sudanese Red Crescent.
Food supplies are rapidly dwindling, with the World Food Programme saying it only has enough stockpiled to feed 23,000 people for ten days.
Researchers said many people have been forced to supplement their dwindling food aid with wild berries and leaves.
South Kordofan borders South Sudan, which broke away from the north last month to become an independent nation.
It has a large population of ethnic Nuba groups, many of which are linked to the Sudan People's Liberation Movement (SPLM), the rebel group which fought the north for decades.
SPLM fighters and other armed groups in southern Sudan have also been linked to widespread human rights abuses.
The 2005 Comprehensive Peace Agreement between north and south requires "popular consultations" this year on South Kordofan's status, but that process has not yet begun.
Khartoum announced a two-week ceasefire in South Kordofan earlier this month.