The two main parties in the coalition accused Sushila Karki of interference after the Supreme Court last month overturned the government's choice for chief of police.
"We have decided to impeach Chief Justice Sushila Karki... after she visibly started taking sides in cases," Min Biswakarma, a member of the ruling coalition who proposed the motion, told AFP on Monday.
Hours later, Deputy Prime Minister Bimalendra Nidhi resigned in protest. One of the smaller coalition parties has also threatened to quit the government.
Karki's supporters say she has taken a strong stance against corruption during her year-long tenure as head of the supreme court.
A committee will now be established to investigate the allegations of bias, after which parliament will vote on whether to impeach her.
But the process is unlikely to get that far as she is due to retire in June when she turns 65.
The government had appointed Jaya Bahadur Chand as police chief, but the court ruled that the highest-ranking officer Navaraj Silwal should take the top job.
The impoverished Himalayan country has had nine governments since the end of the civil war in 2006, with each successive administration seeking to fill key positions with their loyalists.
Political analyst Lok Raj Baral said the coalition government was held together only by the desire of its constituent parties to stay in power.
"There is constant bargaining (within the parties) for them to strengthen their position," he told AFP, describing the impeachment of the chief justice as another attempt to remove any obstacles.
Local elections are due later this month, followed by provincial and then national elections by the end of the year.
The parties that make up the current coalition are expected to perform badly as disillusionment mounts with the constant political bickering and slow pace of change.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)
Subscribe to our YouTube channel, like us on Facebook or follow us on Twitter and Instagram for latest news and live news updates.