A Russian warship violated NATO waters twice on Friday morning, the Danish Armed Forces said.
The Kremlin vessel entered Danish waters north of the Baltic Sea island of Bornholm at 12.30am and again a second time a few hours later.
Denmark branded the move an unacceptable provocation, although the Russian embassy in Copenhagen said the Danes provided no evidence.
Denmark's armed forces said the warship left after the Danish navy established radio contact.
It comes after despot Vladimir Putin warned he was ready to use nuclear weapons to protect Russia's sovereignty.
Denmark's Foreign Minister Jeppe Kofod tweeted: "A deeply irresponsible, gross and completely unacceptable Russian provocation in the middle of #fmdk (Democracy Festival of Denmark)."
The annual Democracy Festival of Denmark is attended by senior government officials, including Mr Kofod and Prime Minister Mette Frederiksen.
"Bullying methods do not work against Denmark," Mr Kofod said.
He said the Russian ambassador had been summoned, which was confirmed by the Russian embassy in Copenhagen.
The ambassador was told that a Russian warship had "allegedly entered into the territorial sea of Denmark," the embassy said in a statement.
"No evidence of what happened, including the coordinates of the alleged crossing of the Danish maritime border by the ship, was presented," the statement said.
There had been no immediate threat against the festival or Bornholm, Danish defence minister Morten Bodskov told local media.
"We must accept that the Baltic Sea is becoming a high-tension area," Mr Bodskov said.
Ukraine's defence minister said last month that Kyiv had started receiving Harpoon missiles from Denmark, deliveries that he said were the result of cooperation between several countries.
Western allies are supplying Ukraine with weapons to defend against Russian forces who invaded in late February.
On Friday, Ukraine said its forces hit a Russian naval tugboat with two Harpoon missiles in the Black Sea, the first time it has claimed to have struck a Russian vessel with Western-supplied anti-ship weapons.
It comes after Putin said he was ready to use nuclear weapons to protect Russia, although he emphasised that he was not threatening the world.
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He said: "One irresponsible politician would blurt something out, then another - at a very high level, by the way, at the level of, say, the Ministry of Foreign Affairs, the top officials there are holding forth on this subject.
"And we’re supposed to say nothing? We answer accordingly. As soon as we answer, (everyone) latches onto that: ‘Look, Russia’s issuing threats!’
"We are not threatening. But everyone needs to know that we have it and we will use it if necessary to protect our sovereignty."
