Drakeford said without changes there could be between 1,000 and 1,700 preventable deaths over the winter.
Businesses will be allowed to provide a takeaway service after 18:00 for food or non-alcoholic drinks.
Traders described the news as a “major blow” to indoor entertainment and hospitality firms.
Drakeford said: “I am very grateful for everything the sector has done.
“I know these new restrictions will be difficult, coming as they do at the one of the busiest times of the year for the sector.
“Unfortunately, we continue to face a virus which is moving incredibly quickly across Wales and a virus that will exploit every opportunity when we spend time with one another.”
The restrictions come into effect at 18:00 on Friday, and are similar to the restrictions on hospitality within level three areas in Scotland.
The decision will be reviewed on 17 December. As well as cinemas, bingo halls, bowling alleys, soft play centres, casinos, skating rinks and amusement arcades will have to close.
Meanwhile current restrictions on travel into England, implemented while a lockdown is in place over the border, is being reviewed.
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