Zambian President Edgar Lungu announced the plan on Monday, which his spokesman said followed a number of breaches of the terms of the licence, without giving details.
Zambia, Africa's second-biggest copper producer, has also proposed tax changes that Lungu says he will push through, despite opposition from international miners which say they will deter investment that Zambia desperately needs.
Some miners have already reduced or threatened to cut output, although First Quantum said it had abandoned plans to lay off workers. Union leaders on Monday called on Glencore to reverse its decision to close two shafts.
"We are not shaken in our resolve to divorce (from some companies), starting with KCM, and we have filed that notification," Lungu said on Zambia National Broadcasting Corporation radio.
The plan mirrors moves in other parts of Africa, where countries are trying to secure greater benefits from natural resources being managed by foreign companies.
Vedanta said it was seeking an urgent meeting with Lungu over the future of KCM and that it had not received formal communication from the government on KCM.
It said in a statement it was the intention of KCM and Vedanta, its primary shareholder, to continue to engage with the government "in a constructive and transparent manner".
The government, which also has a stake in KCM through a state mining company, "(is) fully apprised of and party to the circumstances of the company and major decisions that have been taken," Vedanta added.
Presidential spokesman Amos Chanda told Reuters a notice had been issued to KCM in April last year over a number of breaches of the terms of its licence and it had not convinced the government it should keep the licence.
He also said "about three investors" whom he declined to identify were interested in the asset, but no formal negotiations had begun.
Demonstrators marched in Chingola in Zambia's copper belt to welcome the decision to bring in another investor.
Mine Workers’ Union of Zambia (MUZ) President Joseph Chewe called on the president to bring in "a credible investor, not Chinese", with public opinion turning against China's extensive asset ownership in the country.
He also said the decision on Vedanta should "send a strong signal to other mining companies", and urged Glencore to rescind its plan to close two mine shafts at Mopani Copper Mines, which Glencore has said have reached the end of their economic life.
Neither Glencore nor First Quantum had any comment on Monday.
(Reporting by Chris Mfula in Lusaka and Barbara Lewis in Johannesburg; additional reporting by Ernest Scheyder in Houston, Writing by Alexander Winning; Editing by Louise Heavens and Mark Potter)
By Chris Mfula