In power since 2019, Frederiksen has benefited in recent months from her resistance to Trump's desires to control the Arctic island, but many Danes have grown weary of her focus on international affairs and accused her of neglecting domestic woes.
A poll from broadcaster DR and Epinion gave the left-wing bloc 83 seats against 78 for the right in the 179-seat assembly, the Folketing, while a TV2 and Megafon survey predicted 86 seats for the left and 75 for the right.
The exit polls on Tuesday indicate the worst result for Frederiksen's Social Democrats since the start of the last century, with support collapsing to between 19.2 per cent and 21 per cent, a dramatic fall from the 27.5 per cent they won in the last election.
Partial results are expected later in the evening.
If official results confirm the outcome, Frederiksen may struggle to form a cabinet. She will likely need support from across the political spectrum, similar to her outgoing cabinet, Denmark's first to bring left- and right-wing parties together in more than four decades.
Frederiksen, 48, had campaigned on a promise that her tough and tested leadership skills would help the Nordic nation of six million navigate a complex relationship with Washington and a European response to Russia's war against Ukraine.
In Brussels, she is widely respected for her clear line on Greenland and for her efforts to ramp up Denmark's defence spending in the wake of the Ukraine conflict. But her negotiating style is seen by some as abrasive and many Danes sought change.
Frederiksen called the vote months before an October deadline, in what analysts said was an effort to capitalise on an uptick in popularity when Trump's rhetoric about controlling Greenland, a semi-autonomous Danish territory, intensified in January and he refused to rule out military force.
But Greenland has since moved to a less heated diplomatic track and has been overtaken by domestic concerns, including a proposed wealth tax, debates on immigration and calls for restrictions on agricultural pesticides affecting the groundwater.
"The environment is the most important. And also to have a stable government. That's the two main things I'm voting for," said Kenneth Gall, a theatre producer casting his ballot at Copenhagen's City Hall.
In Greenland, the election is being closely watched, with many hoping it will be a chance for the territory to leverage Trump's attention to wrangle concessions from its former colonial power.
Frederiksen may have to rely on deputies further to the right on the political spectrum or even on a handful of lawmakers from Greenland or the Faroe Islands, both semi-autonomous Danish territories.
This could give Foreign Minister Lars Lokke Rasmussen's non-aligned centrist Moderates the power to decide whether Frederiksen's left-wing bloc or its right-wing opponents form the next government.
