Amnesty, which said it interviewed 120 workers, alleges that many of them worked long hours for low pay and without adequate safety equipment. The palm oil from these plantations could be traced to nine multinational companies, it said.
"Despite promising customers that there will be no exploitation in their palm oil supply chains, big brands continue to profit from appalling abuses," said Meghna Abraham, senior investigator at Amnesty.
The NGO said it chose Wilmar as the focus of its investigation as the company is the world's largest processor and merchandiser of palm and lauric oils, controlling more than 43 percent of the global palm oil trade.
Other companies operating palm plantations in Indonesia include Golden Agri-Resources Ltd , Indofood Agri Resources Ltd and PT Astra Agro Lestari Tbk .
Even though Indonesia had strong labour laws under which most of the abuses can amount to criminal offences, these laws were poorly enforced by the government, Amnesty said.
Wilmar said it welcomed the NGO's report, which helps to highlight labour issues within the broader palm oil industry, but added that finding a solution requires collaboration between governments, companies and civil society organizations.
(For Wilmar's full statement, click http://bit.ly/2fx0q1t)
"We acknowledge that there are ongoing labour issues in the palm oil industry, and these issues could affect any palm company operating in Indonesia," it said.
"The focus on Wilmar ... is often used to draw attention to problems in the wider palm oil industry."
Indonesia is the world's biggest producer of palm oil, used in everything from snacks and soaps to cosmetics and biofuels, with the sector employing millions of workers. But plantation operators say it is difficult to have complete oversight of labour conditions.
No company would "consciously" hire underage labour as that is against the law, but some plantation workers get their children to help out, Sumarjono Saragih, an official at the Indonesian Palm Oil Association, told Reuters by telephone.
"If children want to help their parents, companies cannot forbid that."
Agus Justianto, an official at Indonesia's environment ministry, said that a company found guilty of labour violations could get its permit revoked, but it is "not in the environment ministry's domain."
Indonesia's manpower ministry did not immediately provide comment.
In an emailed statement, U.S. snack and breakfast food company Kellogg Co said it is committed to ensuring that its palm oil is obtained from "known and certified sources that are environmentally appropriate, socially beneficial and economically viable."
If Kellogg finds or is made aware of any supply chain violations, it would discuss corrective actions with its suppliers, it said. "If the concerns are not adequately addressed, we take action to remove them from our chain."
Unilever said while significant progress has been made to tackle environmental issues associated with palm cultivation, more needs to be done to address "these deeply concerning social issues" and promised to work with its partners.
Nestle and Procter & Gamble did not immediately provide comment.
(Reporting by Eveline Danubrata and Bernadette Christina Munthe in JAKARTA; Additional reporting by Masayuki Kitano in SINGAPORE; Editing by Tom Hogue)