Ken Skates, whose constituency in the Welsh Assembly includes large parts of the Shropshire border and towns such as Chirk and Llangollen, says he will be meeting local leaders to find ways of stopping a lockdown.
There are currently two million people in Wales under tight restrictions as part of local lockdowns - currently confined to the south of the country.
Mr Skates, who is also Wales' economy minister says he’s hoping local lockdowns in north Wales can be avoided.
He said the contact tracing system helped contain the virus in Wrexham over the summer and hopes a similar reduction in figures will now be seen elsewhere.
“Obviously some parts of north Wales are registering higher numbers than other areas, but there is no doubt based on what I'm hearing from local authority leaders in the north, that while people are concerned about the coronavirus, people are acting responsibly and responding to the need to act in a way that prevents a further spread of the virus," he said.
“But we will be discussing this issue with local leaders in the north of Wales before reaching any decision on whether local lockdowns are required in any of the six local authority areas.”
Public Health Wales said there were areas of concern, including four council areas in north Wales.
"We are watching the data from there carefully, but numbers of cases are increasing in all parts of Wales so there is no room for complacency in any area," Mr Skates said.