The Danish Energy Agency granted the permit which covers a 147-km (91-mi) long route section.
Preparatory works, such as the installation of concrete mattresses and rock placement for the crossing of existing infrastructure (cables and pipelines), and the subsequent pipelay, will start in the coming weeks.
The Danish section of the pipeline will be built with pipes currently stored in Mukran, on the German island of Rügen.
Nord Stream 2 AG added that more than 2,100 km (1,305 mi) of the pipeline has been laid. Pipelay has been completed in Russian, Finnish and Swedish waters, and for the most part in German waters.
The construction of both landfall facilities in Russia and Germany is nearing completion.