The ministry last week gave the go-ahead to the telecoms regulator to start the process, he said in a recorded response to questions this week.
The new carrier could be in place over the next six to 12 months and the country might even have capacity for a fifth operator, he said.
The local unit of India’s Bharti Airtel and state-owned Zamtel make up the current trio. Communication costs in Zambia had been “rather on the high side,” Mushimba said from Lusaka.
“The market analysis we have done supports the fact that we can have a fourth licensee (in the country) and possibly a fifth and still the market will be profitable.”
Zambia’s search for a fourth operator represents a rare opportunity for international wireless carriers to expand in sub-Saharan Africa without making an acquisition.
Slowing economic growth and falling tax revenue have limited the need for new providers.
Ethiopia is the only significant market that had not opened up spectrum to a private bidder.
Some companies, including Airtel and Millicom International Cellular have made a partial retreat by selling off country units.
Africa’s second-biggest copper producer, with a population of more than 16million, had 12.4million active mobile subscribers at the end of June, 10percent more than a year before, according to data from the finance ministry.
The country had 5.9 million internet users by the end of June, a 3percent rise from the figure at the end of December. Almost all of these use mobile internet.
MTN Zambia had the country’s largest market share of about 48.3percent last year, while Airtel Zambia had 41.4percent, according to the finance ministry’s economic report for that year.
Vodafone Zambia began offering data services in partnership with Afrimax last year, but doesn’t yet have a licence to offer voice calling.
The nation’s telecoms regulator approved a modernised licensing framework this year, opening the way for new operators, Mushimba said.
MTN, based in Joburg, is the continent’s largest wireless operator by sales and customer numbers.