The Danish Foreign Ministry said it had summoned the Russian ambassador for talks on Monday after a Russian aircraft violated Denmark's airspace.
"This is completely unacceptable and particularly worrying in the current situation," Foreign Minister Jeppe Kofod said on Sunday.
Both Denmark and Sweden allege that a Russian AN-30 propeller plane entered their airspace on Friday night, when the aircraft was flying east of the Danish Baltic Sea island of Bornholm, which lies off Sweden's south-eastern coast.
Since the Russian invasion of Ukraine more than two months ago, there has been intense debate in Sweden, as well as in neighbouring Finland, about joining NATO.
Russia has repeatedly warned the EU's two northernmost states against such a move. Denmark is already a member of the Western military alliance.
Concerns were raised in early March when four Russian fighter jets penetrated the airspace over Sweden.