The department alleges that the funds were "misappropriated" and though it did not name PM Najib Razak directly, he is identifiable in the suit as someone whose account allegedly received huge sums.
He has in the past denied wrongdoing.
Mr Najib set up 1MDB in 2009 to turn Kuala Lumpur into a financial hub, but it missed debt payments in 2015.
The US justice department alleges the "misappropriated" funds financed lavish lifestyles of "multiple individuals including public officials".
There is no allegation that Mr Najib spent any of the money but people close to him are accused of using billions of dollars to buy jewellery, art and luxury properties; pay gambling expenses; and hire musicians and celebrities to attend parties.
Malaysia's 'most investigated' company
1MDB: The case that's riveting Malaysia
The court papers, filed in Los Angeles, allege that money was laundered through accounts in the US. If successful the US justice department would seize assets, including property in the US, UK and Switzerland.
The $1bn would only make up a proportion of the money that was allegedly diverted, which comes to more than $3.5bn (£2.6bn).
Mr Najib's stepson, Riza Aziz, is named in the court papers, which were filed in Los Angeles. Mr Riza produced the Leonardo DiCaprio film The Wolf of Wall Street.
A Malaysian financier and two Abu Dhabi government officials are also among those named.
A spokesperson for the prime minister said: "The Malaysian Government will fully co-operate with any lawful investigation of Malaysian companies or citizens in accordance with international protocols.
"As the prime minister has always maintained, if any wrongdoing is proven, the law will be enforced without exception."
The fund started to attract attention in early 2015 when it missed payments for the $11bn it owed to banks and bondholders.
The Wall Street Journal (ESJ) reported it had seen a paper trail that allegedly traced close to $700m from the troubled fund to Mr Najib's personal bank accounts.
1MDB said in a statement last year that it had never given money to the prime minister and called the claims "unsubstantiated". It has repeatedly stated that the company has assets worth more than its debts.
Mr Najib has denied taking money from 1MDB or any public funds.

The adder's-tongue spearwort is only found in two places in the UK - Badgeworth, near Gloucester, and on Inglestone Common, near Bristol.
At Badgeworth, the tiny nature reserve boasts a small crop of the plant but in South Gloucestershire the buttercup is only spotted once every five years.
Plant expert Richard Lansdown said: "We wouldn't normally reintroduce but Inglestone is down to a single plant."
The species, more commonly known as the Badgeworth buttercup, relies on bare, wet ground that has been churned up by cattle to set seed and thrive.
But with fewer animals grazing the common in recent years, it has become overrun with scrub and the buttercup now "only grows intermittently" at a single pond.
"I sieved out the mud and extracted all the seeds [at Inglestone] and didn't find any from the Badgeworth buttercup - there weren't any left at all," said Mr Lansdown.
"So we've had to use seed originally collected from the site some years ago that was sent to the Millennium Seed Bank."
Using the 270 plus seeds held at Kew, 200 plants were propagated and about 80 planted out at Inglestone with a further planting planned for mid-June
"The two sites have been declining for a very, very long time," said Mr Lansdown.
"But we've planted out 83 plants in different locations at Inglestone and at least half of them are surviving and doing well and have begun fruiting which will add to the seed bank."
The US Department of Justice has moved to seize more than $1bn (£761m) from Malaysia's state fund 1MDB.
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A rare buttercup is being reintroduced in South Gloucestershire.