Chitalu Chilufya said 76 of 85 reported new cases in the northern town were either sex workers or lorry drivers.
“Sex workers have been very co-operative and they are giving us all the leads we want,” Mr Chilufya said.
Zambia has confirmed 267 Covid-19 infections, with seven deaths.
Last week, President Edgar Lungu announced the reopening of restaurants, casinos and gyms after a month-long shutdown to enforce social distancing measures.
“The situation in Nakonde remains grave, and the president is concerned,” Mr Chilufya said on Sunday, adding that Mr Lungu had ordered the border to be “temporarily closed.”
Nakonde streets are usually lined by lorries leaving Zambia or entering from neighbouring Tanzania, the BBC’s Kennedy Gondwe in Lusaka reports.
Lorry drivers are seen as a high-risk group because they stop at several towns along the way and are known to have multiple sex partners, he added.
“They [sex workers] are being very co-operative in our investigations, and we don’t want to stigmatise or discriminate against them. They are being very useful in contact tracing,” Mr Chilufya said.
“We had a case where one of them appeared with symptoms and told us about a client who was a lorry driver of foreign jurisdiction and even gave us a contact number. We called that number and we were told the person we called had Covid-19,” the minister added.
Health authorities in East Africa have expressed concern that lorry drivers, listed as essential workers, could be spreading coronavirus.
Strict checks, including tests by Ugandan authorities, have caused long tailbacks at its border with Kenya.