That's true for, say, bread. Or really any fungible good where labor makes up most of the price of the product. If you artificially suppress those prices, there isn't enough money to pay the farmers and bakers, and no bread will be made.

This freeze actually exempts new construction, so the whole problem is mood. But it's still interesting to think it through, and the result is different than simple economics may make you think:

Housing is different than bread, or cars, or mobile phones. It doesn't actually cost meaningfully more to build a new house in the middle of Berlin than to do so in some empty village in the countryside: the costs of material are the same, and for the most part so is labor.

The only difference is the cost of land.

The effect, according to the basic supply/demand scheme of economics you are invoking should be to depress land value, with no effect on the amount of housing units being built. That's true as long as the rent it is possible to charge is high enough to cover the costs of construction. One can take a guess at the actual value by looking for the cheapest rents in newly constructed housing, which for Germany is about half of Berlin's average. In the limit, land value would tend toward zero, although that's rather theoretical because at some point owners just wouldn't care about selling.

This hints at some additional factors that may have minor impact: maybe there is an expectation that land value will rise again after those five years, and the actual discount in the market is therefore smaller, etc. But even then, it's only land value that would be affected.