The move is in line with UN sanctions aimed at curbing Pyongyang's nuclear weapons capability.
German media say City Hostel Berlin is run by a Turkish hotelier who pays more than €38,000 (£32,000; $41,000) a month in rent to North Korea.
The embassy also derives income from a conference hall at the site.
North Korea has conducted several nuclear tests and launched missiles, provoking fears that it could one day hit Japan or the US with a long-range nuclear strike.
German Foreign Ministry spokesman Martin Schäfer said "any kind of commercial activity on the site of the embassy or in relation to the embassy is prohibited".
"City Hostel in Berlin constitutes neither a diplomatic nor consular activity of a North Korean foreign representation," he said, adding that the government will move to "shut down the financial source to the North Korean regime as quickly as possible".
Germany's Berliner Zeitung newspaper says (in German) the ministry has warned the leaseholders that they must end their contracts with North Korea - otherwise they face hefty fines.
City Hostel Berlin was built in former communist East Germany and at the time housed North Korean embassy staff.
It is a popular budget option for travellers to Berlin, who can stay in an eight-bed dormitory room for just €9.50 per night.
The business relationship with North Korea was not confirmed by hostel staff, German media said.
UN Resolution 2321, adopted unanimously in November, tightened sanctions on North Korea, in response to Pyongyang's 9 September nuclear test.
It includes a clause stating that "all Member States shall prohibit the DPRK [North Korea] from using real property that it owns or leases in their territory for any purpose other than diplomatic or consular activities".
Markus Ederer, state secretary at the German Foreign Ministry, said "we must step up the pressure in order to bring North Korea back to the negotiating table".
The UN sanctions must be implemented to the letter, he said, "so it is especially important that we act to cut off the activities funding the nuclear programme".

He told the BBC he was hopeful the party could get "over the line in a number of seats".
But he would not be drawn on how many seats, or in which constituencies.
The party is standing in about half the number of seats contested in 2015. Its only MP in the last parliament, Douglas Carswell, defected in March.
Mr Nuttall said UKIP was campaigning strongly in seats where it has local councillors.
And he rejected suggestions the party was in decline, predicting that by the end of 2018, UKIP would be "bigger in terms of membership and higher in the polls than it's ever been before".
Asked about suggestions support for UKIP could cost the Conservatives seats, he told BBC Radio 2's Jeremy Vine he had struck deals with Brexit-supporting MPs from both the Tories and Labour, to help them retain their seats:
"In some places we have stood down in favour of a Labour MP," he said.
"People like Kate Hoey, for example, I don't want to see Kate Hoey not in the House of Commons because she's been a true Brexiteer all her life.
"What we need is for the prime minister to go into these negotiations strong, confident in our country and not prepared to backslide."
He also spoke about the Manchester attack and said that while the prime minister was not to blame for last week's bombing, Theresa May was responsible for cutting police numbers
Local police officers who are known in a neighbourhood were more likely to have the trust of the locals who would pass information to them, he said.
He also talked about banning Muslim women from wearing a full face veil.
He said he was "serious" about banning the veil in the UK and claimed that other countries in Europe were also going the same way.
He said such a ban was needed for greater integration, so that people could be identified on CCTV and also because of vitamin D deficiency.
German authorities plan to terminate a North Korean business in the heart of Berlin - a big hostel next to the communist state's embassy.
[NEXT_CONCEPT]
UKIP will win seats at the general election, even though they had no MPs at the end of the last parliament, its leader Paul Nuttall has predicted.