Vaughan Gething told journalists the situation was “very serious” and said health services were coming “under considerable and sustained pressure”.
He said the country was the only part of the UK where figures were not falling at the end of November.
Public Health Wales recorded a further 2,021 coronavirus cases today, the first time the country has recorded more than 2,000 new cases in a day. A week ago, the number was 802 cases a day.
Wales’ health minister said it would take a couple of weeks for these new rules to impact the virus case rate.
He said: “We’re actively considering each day whether the measures we have are the right ones in place or not.
“We’re committed to review the regulations in the next week and a half or so and we will then have to consider what we do.
“We’re actively considering what we are going to need to do, what we may need to do after the Christmas period.”
Gething added: “If we do not see a reduction in coronavirus [hospital] admissions, we will need to consider what action we can take and may need to take to support the NHS as we move into the New Year.”
The alcohol ban will be reviewed on 17 December.
“I would not even break even staying open,” operator Barrie Walden told The Morning Advertiser of his decision to close his pub during the ban.
“We will miss the valuable trade that gets us through the quiet January and February.”