The money would be used to build infrastructure, including roads and railways, Emmanuel Ibe Kachikwu said.
Militant attacks have severely disrupted oil production, fuelling a recession in the West African state.
The militants have been demanding that the government spend more of its oil wealth on tackling widespread poverty in a region, known as the Niger Delta.
They also accuse multinational firms of polluting the environment, destroying the livelihoods of farming and fishing communities.
Mr Kachikwu said that President Muhammadu Buhari would meet the militants and community leaders next week.
"Our target is to ensure zero militancy in the area," he said.
"This planned meeting shows the level of interest the president has to ensure peace in the area."
The $10bn would "not necessarily" come from the federal government, but from "oil companies, investors, individuals", he is quoted by Reuters news agency as saying.
A new militant group, the Niger Delta Avengers (NDA), emerged after President Buhari, a northerner, took office last year after winning elections.
It has carried out a spate of attacks on oil plants and pipelines, causing a sharp fall in oil production and worsening the financial crisis in Africa's most populous state.
Mr Buhari's predecessor Goodluck Jonathan came from the Niger Delta, and managed to broker a peace deal with militants in the region.
The militants accuse Mr Buhari of reneging on the deal, an allegation he denies.
Oil is the Nigerian government's main source of income.
Nigeria will invest $10bn (£8bn) in its oil-rich south to end an insurgency by militants, the oil minister has said.