Ahead of an emergency summit in Brussels today, interior minister Thomas de Maiziere said refugees could “not choose” their host countries and called on other EU states to do more.
Officials in Munich said they were struggling in their attempts to house refugees after 13,000 migrants arrived in the city on Saturday.
Germany and Austria agreed over a week ago to let in migrants who had gathered in Hungary, saying it was a one-off measure to ease an emergency.
But the influx has continued and German officials said over the weekend that the speed of the arrivals was straining the country’s ability to provide accommodation.
“Germany is temporarily introducing border controls again along (the EU’s) internal borders. The focus will be on the border with Austria at first,” Mr de Maiziere told a news conference.
“The aim of these measures is to limit the current inflows to Germany and to return to orderly procedures when people enter the country.
“This step has become necessary,” he added. “The great readiness to help that Germany has shown in recent weeks . . . must not be overstretched.”
Mr de Maiziere did not specify how long the border controls would remain in place or give details of exactly how incoming migrants would be handled.
He did say there could be disruption to rail travel.
Germany’s national railway, Deutsche Bahn, said it had halted services between Austria and Germany for 12 hours on the authorities’ orders.
Hungarian police say more than 186,000 people have passed through Hungary from Serbia this year en route to Austria and the migrants’ major destination, Germany, which says it has taken in more than 50,000 newcomers in the past week alone.
About 450,000 migrants have arrived in Germany this year. The country is expecting at least 800,000 in 2015 - by far the most in the 28-nation EU.
In another tragedy on Sunday, at least 34 people drowned as they attempted to cross from Turkey to Greece.
Such risks have not deterred scores of boats to make the daily crossing to Greece’s eastern islands, from where migrants pursue a more than 1,000-mile journey to the heart of the European Union via the Balkans and Hungary, where authorities have vowed to fortify their southern frontier and prosecute those who try to evade border police.
Hungarian army engineers spent yesterday expanding the country’s planned 109-mile border fence with Serbia as the government warned that, from tomorrow onwards, any asylum seekers caught breaking through the barrier would be arrested and charged with a criminal offence.
Police said 4,330 were detected crossing on foot in the previous 24 hours, 700 more than the previous one-day record, as trekkers strove to reach Hungary before the tougher security measures take effect.
Hungarian Prime Minister Viktor Orban said he is determined to make his country a more difficult challenge, with deployments of troops and potential prison terms part of the deterrent.
Meanwhile, Austrian police said they rescued 42 people, including five women and eight children, from a refrigerated lorry on a highway near the border with Germany.
Police in Upper Austria province say the migrants were found yesterday morning at a rest stop on the A8 highway at Aistersheim by officers looking for traffickers’ vehicles.