The route between Harwich, Essex and Esbjerg in Denmark, run by DFDS Seaways, has been in operation for nearly 140 years.
The company said the route "has been struggling for a long time" and would not be able to take on costs associated with a new environmental law.
The final ferry is to sail on Sunday.
Chief executive of DFDS Seaways, Niel Smedegaard, said: "The route is of particular historical significance to DFDS so it's a very sad day for us all.
"Our regrets go to our many passengers who must now see the last passenger ferry route between the UK and Scandinavia close."
How popular are ferries?
•Last year, 20.5 million people used ferries to travel abroad from the UK - the first year on year increase since 2010
•One of the most popular routes, between Dover and Calais, has had car ferries running since the 1930s
•The number of passengers travelling from ports on the East Coast fell last year for the third consecutive year, to 2.2 million
•A number of passenger routes linking Norway and Newcastle ceased running in 2008
•Ferries between Harwich and Hamburg in Germany were stopped in 2002
•Stena Line runs a ferry from Harwich to the Hook of Holland. The line has seen an increase in passenger numbers in recent years
From 1 January 2015, a European Union directive aimed at reducing sulphur dioxide emissions from ships will come into force.
DFDS said this would have resulted in a £2m a year increase in the cost of the Harwich to Esbjerg ferry route.
Mr Smedegaard said the company had not been able to reduce costs enough to enable the route to bear the extra charges.
In June last year, the Sirena Seaways vessel running the Harwich-Esbjerg route hit the quay while docking and started to let in water.
There were 489 passengers on board, but no-one was trapped or injured.
The crash caused severe damage to the quay and holed the ferry in several places, some below the waterline.
An investigation found one of the ship's back-up systems was keeping an engine running at 63% power when it was approaching the dock.
This prevented tugs from moving the vessel so passengers could disembark safely.
At the time, DFDS said changes were made to stop such an accident happening again.

Ford, like most of its rivals, is seeking ways to profit as the industry moves toward driverless technology and ride-sharing.
The company also added it would move all of its small-car production from Detroit to Mexico within three years.
Shares of Ford dropped more than 1.5% after it announced its 2017 outlook.
The share price has not recovered since it fell more than 8% in late July when Ford said the industry was going into a gradual decline.
Last week, Ford lowered its 2016 pre-tax profit forecast to $10.2bn from at least $10.8bn because of an expanded vehicle recall.
It had initially forecast a profit equal to or better than last year, but pulled back after announcing a $640m recall of 2.4 million vehicles.
Ford currently makes some Fiestas in Mexico, but has kept production for some of its Focus and C-Max models in suburban Detroit.
The company is building a new $1.6bn assembly plant in San Luis Potosi, Mexico. It will make small cars there starting in 2018.
The move has drawn criticism from presidential candidate Donald Trump, would complained about a loss of US jobs. Ford chief executive said during an investor day on Wednesday that the company had to stay competitive.
Ford's Michigan Assembly Plant will be getting new products under a contract signed last year with the United Auto Workers union.
The UK's only ferry link to Scandinavia is to close for good, marking the "the end of an era", its operator says.
[NEXT_CONCEPT]
US carmaker Ford has said it expects pre-tax profits to fall next year as it increases spending on projects such as self-driving and electric cars.