Economic Empowerment Secretary George Magosvongwe issued the warning in parliament, state media reports.
“Indigenization” of the economy was one of President Robert Mugabe’s main campaign themes in the March election.
Farming, hairdressing and baking are among the sectors now reserved for “indigenous,” or black, Zimbabweans.
“January is a month to come and we are putting in place measures for enforcement in the event that they do not comply,” the state-owned Herald newspaper quotes Mr Magosvongwe as saying.
He said that Zimbabweans were being identified to take over businesses to prevent shortages of goods.
According to the Herald, the “reserved sectors of the economy” include: retail and wholesale business, hairdressers, beauty salons, bakers, employment agencies, agriculture, transport, estate agencies and advertising agencies.
It said that foreign-owned restaurants that did not serve local food would not be affected.
Owners of businesses without indigenization compliance certificates face a fine or imprisonment if they are still operating, the Herald reports.
It says these certificates are only given to local people.
There has been growing concern in Zimbabwe over an influx of traders from Nigeria and China who sell all sorts of goods in local markets, undercutting local retailers.
Mugabe says his policies are needed because under colonial rule, many economic sectors were reserved for white people.