Her comments came in response to US President Donald Trump's renewed call for the strategic, mineral-rich Arctic island to come under US control in the aftermath of the weekend military operation in Venezuela.
The dead-of-night operation by US forces in Caracas to capture leader Nicolas Maduro and his wife early Saturday left the world stunned, and heightened concerns in Denmark and Greenland, which is a semi-autonomous territory of the Danish kingdom and thus part of NATO.
Frederiksen and her Greenlandic counterpart, Jens Frederik Nielsen, blasted the president's comments and warned of catastrophic consequences.
Numerous European leaders expressed solidarity with them.
"If the United States chooses to attack another NATO country militarily, then everything stops," Frederiksen told Danish broadcaster TV2 on Monday.
"That is, including our NATO and thus the security that has been provided since the end of the Second World War."
Trump called repeatedly during his presidential transition and the early months of his second term for US jurisdiction over Greenland, and has not ruled out military force to take control of the island.
His comments on Sunday, including telling reporters "let's talk about Greenland in 20 days", further deepened fears that the US was planning an intervention in Greenland soon.
Frederiksen also said Trump "should be taken seriously" when he said he wanted Greenland.
"We will not accept a situation where we and Greenland are threatened in this way," she said.
Nielsen, in a news conference on Monday, said Greenland could not be compared to Venezuela, and urged his constituents to stay calm and united.
"We are not in a situation where we think that there might be a takeover of the country overnight and that is why we are insisting that we want good co-operation," he said.
"The situation is not such that the United States can simply conquer Greenland."
Trump on Sunday mocked Denmark's efforts at boosting Greenland's national security posture, saying the Danes have added "one more dog sled" to the Arctic territory's arsenal.
"It's so strategic right now," Trump had told reporters Sunday as he flew back to Washington from his home in Florida.
"Greenland is covered with Russian and Chinese ships all over the place," he said.
"We need Greenland from the standpoint of national security, and Denmark is not going to be able to do it."
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