The Baltic Sea has been warned that the leak of the gas line from Russia could endanger naval traffic.
There was a prohibitive zone around the Bornholm island.
The energy ministry acted after being told about the pressure drop.
The drop happened overnight, according to the operating company.
It said in a statement that it was investigating the matter after it registered a rapid gas pressure drop on the line.
The majority shareholder of the company is Russia.
There are no security risks associated with the leak outside of the prohibitive zone.
The security of the Danes' gas supply is not expected to be affected.
The multi-billion euro project to deliver gas from Russia to Europe was halted after Russia invaded Ukraine.
There are concerns that large amounts of gas could be released into the atmosphere because gas had already been pumped in.
There has been a shut down of the parallel gas line for several weeks.
Russia denies that it is blackmailing Europe by using its gas supplies to do so.
The price of energy has gone up since Russia invaded Ukraine.
Families in the EU may not be able to afford heating this winter.
Europe is trying to wean itself off of Russian energy in order to reduce Moscow's ability to finance the war.