This is what it says on the ministry's site, so yah you right not citizenship but permanent residency

"To be able to purchase property in Denmark you are required to have either a permanent residence in Denmark or have lived in Denmark for a consecutive period of five years. The permission is obtained from the Danish Ministry of Justice."

I'm pretty sure you can't buy real estate in Denmark unless you are a citizen or have lived there for over 5 years or something along those lines.