According to the Danish Armed Forces, the helicopter was on a routine mission to take photographs in an area south of the town of Gedser on the island of Falster.
When the helicopter was near the Russian warship, two emergency flares were fired, one of which is reported to have passed the helicopter at very close range.
Denmark's Defence Minister Jeppe Bruus (S) says he takes the incident seriously.
This is a sign that the boundaries have been moved when it comes to risk-taking on the Russian side, he says.
The Danish Ministry of Foreign Affairs has summoned the Russian ambassador following the incident. It is unclear when the meeting will take place.
Jeppe Bruus calls the Russian actions unprofessional.
This does not mean that we will change our actions in the sense that we have a completely legitimate task to monitor what is going on, and the Defence Forces will continue to fulfill that task in the future, he says.
No one was reported to have been injured.
