Sweden on Monday imposed controls on travelers arriving from Denmark in a bid to curb an unprecedented influx of refugees, prompting knock-on measures from Denmark that triggered fresh concern for Europe's Schengen passport-free zone.

Hours after the Swedish controls on a major bridge-and-tunnel link with Denmark went into effect, the Danish government, which fears being saddled with large numbers of migrants, announced it would implement spot checks on its border with Germany.

Alarmed by the restrictions, which come as both Germany and Sweden grapple with record migrant numbers, Berlin warned Europe's Schengen zone was "in danger".

"Freedom of movement is an important principle - one of the biggest achievements in recent years," German Foreign Ministry spokesman Martin Schaefer said.

"Schengen is very important but it is in danger," he said.

Swedish Migration Minister Morgan Johansson defended his country's systematic controls, saying they were aimed at "preventing an acute situation where we can no longer welcome asylum seekers properly".

The new measures mean travelers between the neighboring countries will have to show their ID cards for the first time since the late 1950s, when a Nordic agreement on passport-free travel came into force that predates the 20-year-old Schengen zone.

Danish Prime Minister Lars Lokke Rasmussen cited the Swedish checks to justify his own country's immediate introduction of random border controls. "We are simply reacting to a decision made in Sweden. ... This is not a happy moment at all," he said.

Rasmussen warned that Sweden's controls could have a domino effect on Denmark, which received just 21,000 asylum requests in 2015, compared to Sweden's 163,000.

"It's clear the EU is not able to protect its outer borders and other countries are going to be forced to introduce ... border controls. Europe's leaders must react to this," he said.