The 4 percent stake is valued at nearly 9 billion rupees ($163 million) at current market price, but New Delhi is expected to offer shares at a discount to the market price to lure investors.
The federal cabinet approved the sale of 9.5 percent in Hindustan Copper in September. Mohd. Haleem Khan, secretary at the department of divestment, said the stake sale on Friday would be the first step.
The government owns 99.59 percent of Hindustan Copper.
New Delhi plans to sell stakes in miner NMDC Ltd and explorer Oil India before Dec. 20, Khan old reporters.
The government aims to raise 300 billion rupees ($5.5 billion) through share sales in state-run companies in the current fiscal year that ends next March, but has thus far drawn a blank as weak market conditions have deterred public issues or auctions.