The incident occurred in international waters south of Gedser on Monday, when the helicopter was on a routine mission to take photographs, according to the Ministry of Defence.
One of the flare rockets is said to have passed the helicopter at very close range.
Denmark's Defence Minister Jeppe Bruus (S) says he takes the incident seriously.
It is a sign that the boundaries have been pushed 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.
No one was reported to have been injured.
