"The aim of these measures is to limit the current inflows to Germany and to return to orderly procedures when people enter the country.
Mr de Maiziere added: "This step has become necessary. The great readiness to help that Germany has shown in recent weeks... must not be overstretched."
The Interior Minister did not specify how long the border controls would remain in place or give details of exactly how incoming migrants would be handled. He said there could be disruption to rail travel. Most migrants have been arriving by train.
Germany's national railway, Deutsche Bahn, said it had halted service between Austria and Germany for 12 hours at authorities' orders.
The rules of Europe's passport-free travel zone, known as the Schengen area, allow countries to reintroduce controls in exceptional circumstances, and the European Commission said that "the current situation in Germany ... appears to be a situation covered by the rules".
In a statement the EU executive said: "The temporary reintroduction of border controls between member states is an exceptional possibility explicitly foreseen in and regulated by the Schengen Borders Code, in case of a crisis situation."
It added that the executive would keep the situation under review and said the aim would be to return to the normal situation of no border checks between member states of the Schengen zone "as soon as feasible".
The European Commission added: "The German decision of today underlines the urgency to agree on the measures proposed by the European Commission in order to manage the refugee crisis."
It is not yet clear exactly what the temporary measures include, but the move comes as German authorities have warned they are at "the limit" in coping with the migrant crisis, with locals claiming Munich is on the brink of collapse.
German newspaper Bild cited security sources as saying the state government in Bavaria had asked the federal police to help deal with the task.
The newspaper said the federal police would send 2,100 officers to Bavaria to help it secure its borders.
Germany has become the destination for many desperate Syrian refugees fleeing their war-torn home country, after it waived EU rules in August.
Tens of thousands of people have crossed Austria by train on their way to Germany since the two countries threw open their borders to the migrants last weekend. A record number were expected to enter Austria from Hungary on Sunday.
The German government announced the nation would take in applications for Syrian asylum-seekers, regardless of where they first arrived in the EU.
Munich, in Germany's southern state of Bavaria, has been the main entry point for those entering the country.
Some 13,015 refugees arrived in Munich yesterday alone and 1,400 more are expected to reach the city today - but there are fears it is already at breaking point.
A police spokesman in Munich said: "Given the numbers from yesterday, it is very clear that we have reached the upper limit of our capacity."
Federal transport minister Alexander Dobrindt added how 'effective measures are necessary now to stop the influx'.
In a statement, he said: "That includes help for countries from where refugees are fleeing and also includes an effective control of our own borders which also no longer works given the EU's complete failure to protect its external borders."
Christoph Hillenbrand, president of the Upper Bavaria region, said he did not know "how we can cope".
Bavarian public television BR said the city "came very close to a humanitarian disaster", but managed to limit the number of people sleeping on mattresses on the ground to a few dozens rather than the hundreds that was first feared.
German Economy Minister Sigmar Gabriel added: "The European lack of action in the refugee crisis is now pushing even Germany to the limit of its ability."
The authorities are considering whether to open up the Olympiahalle - a stadium used for the 1972 Olympics and which today serves as a concert hall or sports arena - as a temporary shelter for the refugees.
- Daily Mail
