Prime Minister Thorning-Schmidt said there would be a cabinet reshuffle soon but analysts said the government would be weakened by the Socialist People's Party's departure.
"This is a clear weakening of the government," Rune Stubager, professor at Aarhus University's department of Political Science and Government, told Reuters.
He said it will become more difficult for the government to gain parliamentary support for its bills.
The Socialist party, the most leftist of the three parties in the ruling coalition, has struggled to find its place in the government which, since coming to power in October 2011, has cut corporate taxes and unemployment benefits and raised the pension age as part of economic reforms.
The government's planned sale of 25 percent stake in DONG Energy caused a split in the party which party leader Annette Vilhelmsen said on Thursday was not possible to resolve.
"I have aimed at unifying the party, but it has proven not to be possible," Vilhelmsen, who has led the party since October 2012, told a press briefing on Thursday. "We do not wish to be part of a government at all costs," she said.
Vilhelmsen has been in favour of the sale and said at a meeting late on Wednesday that she had gained sufficient support in the party to back the bill, but on Thursday morning she said she would step down as party chairman and the party would leave the government.
Some senior party figures have opposed the plan because it will give Goldman Sachs a veto in key areas such as changes in management and merger and acquisitions. They have also questioned the valuation of the energy group.
A majority of members of the Danish parliament's Finance Committee on Thursday gave the final seal of approval to sell a quarter of DONG Energy.
Vilhelmsen said that her party and its 15 members of parliament would continue to support a government consisting of the two remaining parties in the coalition, Thorning-Schmidt's Social Democrats and the Social Liberal Party.
Those two parties have 61 of the 179 seats in parliament. With continued support from left-wing party Red-Green Alliance which has 12 seats, as well as three members of parliament from Denmark's overseas regions Faroe Islands and Greenland, and an independent member of parliament, the two parties have sufficient support to remain in power.
"I expect that the Socialist People's Party and the government will continue to have a close and confidential co-operation," Thorning-Schmidt said.
Six of Denmark's 22 ministers are from the Socialist People's Party.
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