The video, believed to date back to November, shows a soldier pouring liquid over the body as others, including one wearing a South African uniform, watch and film the scene on their mobile phones.
An investigation has been opened by regional forces on the possible "involvement of its members in this despicable act", the South African army announced on Tuesday.
The video "is another horrific event that gives a glimpse of what is going on away from the attention of international media in this forgotten war," said Amnesty's east and southern Africa director, Tigere Chagutah."Human rights violations and violations of international humanitarian law are still occurring," it said in a statement.
A bloody jihadist insurgency began in Mozambique's Cabo Delgado province in 2017, prompting deployment of troops from Rwanda and neighbouring countries in mid-2021 to help Mozambique's embattled army.
The insurgency has led to the death of more than 4,500 people, while almost a million have fled their homes, according to NGOs and the UN.
The government has regained control over much of the region since thousands of African troops were deployed in 2021.
But "security in Cabo Delgado must not come at the cost of human rights violations", Chagutah warned.