The metal fence, which will be only five feet high, is intended to keep out wild boar.
Denmark and Germany are both members of the Schengen Area, and there are no border formalities between the two countries. But the right to border-free travel does not extend to wild boar.
The Danish government says it is building the fence to prevent African swine fever ever crossing the border and decimating the country's bacon industry.
It has started construction on the 30.4m krone (£3.5m) fence despite the fact there are no reported cases of the disease in Germany.
"It is an insurance policy against African swine fever. You also insure your house against fire, although it will probably never burn," Mogens Dall, chairman of the Danish agricultural association LandboSyd, told Jyllands Posten newspaper.
African swine fever is harmless to humans but almost always fatal in pigs. It has already spread into Europe and cases have been reported in Belgium, Poland, the Czech Republic, Hungary and the Baltic states.
The Danish government fears an outbreak could have devastating consequences for the country's pork industry. Denmark is the only EU country where there are more pigs than humans, and currently exports around €4bn (£3.5bn) of pork a year.
If African swine fever is detected in the country, all exports will be stopped. "It would mean ruin and unemployment for up to 33,000 people who are employed in the sector," Mr Dall said.
France is planning its own fence against wild boar on its border with Belgium, and boar that stray across are being culled.
But the Danish fence has proved controversial across the border in Germany, where it has come under attack from regional politicians and animal rights activists.
"We have considerable doubts about the usefulness or necessity of a fence," Jan Philipp Albrecht, regional environment minister for the German state of Schleswig-Holstein said, adding that the disease is mainly spread by humans who have handled infected livestock.
Environmentalists warn the fence will also disturb wolves, otters and golden jackals - and argue it will be ineffective against wild boar, who they say will find crossings planned for other species.
"They can run fast at 35 kilometers per hour. They'll find a hole in a few minutes," Bo Øksnebjerg of the World Wide Fund for Nature (WWF), told Schleswig-Holsteinischer Zeitungsverlag newspaper.
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