The four-month-old coalition, led by the Social Democratic Siumut party of Prime Minister Kim Kielsen, lost its parliamentary majority when the left-wing pro-independence party, Naleraq, quit in protest over Copenhagen's direct financial participation in the project.
Naleraq's departure left Kielsen three seats short of a majority in Greenland's 31-seat parliament.
With Denmark's Prime Minister Lars Løkke Rasmussen currently on a visit to the world's largest island, the pro-independence party accused Kielsen of conducting the negotiations without it.
Denmark's aim, in wanting to partly fund the infrastructure projects, was to prevent Greenland's government from having to turn to China's state-owned China Communications Construction Company (CCCC) as a possible partner and investor, said Mikaa Mered, professor for polar economics and geopolitics at the ILERI institute in Paris.
"The implosion of the government comes as no surprise. It just happened earlier than expected, barely four months after the election," Mered said.
Nevertheless, the coalition's collapse did not mean that new elections would automatically have to be held.
Siumut could seek the support of the socialist Inuit Ataqatigiit, with which it had shared power in the previous administration between 2014 and 2018, the expert said.
At the end of April, Siumut narrowly beat Inuit Ataqatigiit, and they failed to form a coalition over differences on fishing -- which accounts for 90 percent of Greenland's exports.
Instead, Siumut formed a coalition with Naleraq and two other parties, Atassut and Nunatta Qitornai.
Plagued by financial and social woes, Greenland with about 56,000 people receives an annual grant of around 3.6 billion Danish kroner (453 million euros) from Copenhagen.