Danish Prime Minister Lars Lokke Rasmussen has said the introduction of temporary controls along the country's border with Germany was necessary to "secure peace and order."
He said the measures will initially be in place for 10 days. They were imposed hours after Sweden instated identity checks for travellers from Denmark.
Police will conduct "spot checks," Rasmussen said. "It does not mean that everyone from Germany will be checked. Police will not ask everyone to show their passports."
The Danish checks were to apply to the land border in southern Jutland, and ferry terminals at Gedser, Rodby and Ronne.
Rasmussen said he had informed German Chancellor Angela Merkel and the head of the northern German state of Schleswig-Holstein, which borders Denmark.
Merkel's spokesman Steffen Seibert said only joint European solutions could solve the migration crisis and not "at national borders between country A and country B."
A Foreign Ministry spokesman in Berlin said that freedom of movement has been one of Europe's greatest achievements in the last 60 years. He warned that the bloc's free-travel Schengen area was at risk because of the influx of refugees.
Several EU countries, including Germany, Austria and Sweden, reintroduced border controls last year to cope with the growing number of migrants and refugees.
"If the European Union cannot protect the external border, you will see more and more countries forced to introduce temporary border controls," Rasmussen told a news conference.
About 200 Danish police officers were to be deployed initially. Danish broadcaster DR reported that a dozen officers were spotted at a border crossing in the southern town of Padeborg.
Since early September, some 91,000 people have passed through Denmark from Germany, of whom 13,000 applied for asylum in Denmark. The others continued to Norway and Sweden, Rasmussen said.
There is a risk that people will be stranded in Denmark if they can't continue to Sweden, he added. Norway stepped up checks in November.
The European Commission said Denmark had in a letter cited "public security and internal order," and EU Migration Commissioner Dimitris Avramopoulos had spoken to Danish officials.
The anti-immigration Danish People's Party that provides parliamentary backing for Rasmussen's right-leaning Liberals said Denmark's move was "a step in the right direction."
But the party's leader, Kristian Thulsen Dahl, called for more checks, saying the Schengen zone has collapsed.
Meanwhile, passengers boarding trains, ferries or buses bound for Sweden have to show a passport or other form of valid ID card to be allowed onboard under the new rules. Transport companies are responsible for conducting the checks.
Similar checks between the two Nordic neighbours have not been in place since the 1950s.
The Danish Transport and Logistics Association that groups 2,100 road hauliers said it did expect the new Danish and Swedish rules to cause delays, a spokesman told dpa.
Danish train operator DSB said it has set up 34 checkpoints at the Kastrup train station that serves Copenhagen Airport, and is the last train stop before the Swedish border.
The checks are conducted after passengers change trains before continuing over the Oresund rail and road bridge that connects Sweden to Denmark.
"We are checking people's ID and have done so since midnight (2300 GMT). We have not experienced any major queues or challenges," DSB spokesman Tony Bispeskov told Danish news agency Ritzau.
Swedish television reported that eight people were stopped at Kastrup in the first seven hours. Four were Afghan nationals without ID papers and were sent back to Copenhagen's Central Station.
Train commuters have protested at the new rules, saying journeys will be made longer. Regional authorities and trade associations warned against bottlenecks and higher costs for integrating businesses and labour markets.
Anna Johansson, Sweden's infrastructure minister, said: "The aim is to reduce the number of people seeking asylum. In 2015, we received about 163,000 people and in the long term we cannot cope with these numbers in order to cope with providing accommodation and schooling."
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