Danish police also closed a motorway between the two countries when some asylum seekers began walking north after being forced off a train.
They say their destination is Sweden.
As the EU struggles with a major migrant crisis, the European Commission has proposed that 120,000 additional asylum seekers should be shared out between members, using binding quotas.
Denmark’s DSB rail operator said trains to and from Germany had been suspended for an indefinite period because of exceptional passport checks.
Promise of papers
Two trains carrying more than 200 migrants are being held in Rodby, a major port with ferry links to Germany. Danish police say many migrants are refusing to leave the trains because they do not want to be registered in Denmark.
Sweden has become a top destination for refugees after it promised to issue residency papers to all Syrian asylum seekers.
Police also closed part of the E45 motorway – the main road link between Germany and Denmark – after about 300 migrants left another train and set off on foot towards Sweden near the border town of Padborg.
More than 1,200 migrants have crossed into Denmark from Germany in recent days.
Both countries are part of the “Schengen group” of European states that allow passport-free travel – although under the scheme border controls can be reimposed in exceptional circumstances.
A surge of migrants fleeing conflict and hardship in Africa and the Middle East has pushed north through Europe over the past few weeks.
Many of those escaping the civil war in Syria have travelled from Turkey across the sea to Greece, through Macedonia and Serbia, and then to Hungary from where they aim to reach northern Europe.
On Wednesday European Commission President Jean-Claude Juncker announced plans for a “swift, determined and comprehensive” response through a quota system.
In a “state of the union” annual address, he said tackling the crisis was “a matter of humanity and human dignity”.
Among Mr Juncker’s proposals:
- EU member states to accept their share of an additional 120,000 refugees, building upon proposed quotas to relocate 40,000 refugees which were set out in May (though governments then only actually agreed to take 32,000)
- A permanent relocation system to “deal with crisis situations more swiftly in the future”
- Commission to propose list of “safe countries” to which migrants would generally have to return
- Efforts to strengthen the EU’s common asylum system
- A review of the so-called Dublin system, which states that people must claim asylum in the state where they first enter the EU
- Better management of external borders and better legal channels for migration
“It’s 160,000 refugees in total that Europeans have to take into their arms and I really hope that this time everyone will be on board,” Mr Juncker told the European Parliament.
The new plans would relocate 60% of those now in Italy, Greece and Hungary to Germany, France and Spain.
The numbers allocated to each country would depend on GDP, population, unemployment rate and asylum applications already processed.
Countries refusing to take in migrants could face financial penalties.