"Unemployment has now reached its 'structural level' ... There are, so to speak, no labour reserves among the unemployed," it said in a quarterly report.
"There are already signs of pressures in the labour market. The clearest indications are reporting of labour shortages in both the construction and manufacturing sectors," it added.
Seasonally adjusted unemployment stood at 4.2 percent in May, roughly corresponding to the "frictional" unemployment that accounts for people spending short periods of time between jobs, it said.
The report identified four groups of people that could be used to expand the workforce: working people pushing back their retirement, students, people on disability pensions and immigrants.
It also warned that the housing market in Copenhagen was in danger of overheating.
"Price increases in Copenhagen have been so persistent and strong that the development could be consistent with a bubble ... just as in the mid-2000s," it said.