The tighter border controls come after the EU's top economy last year took in a record 1.1 million refugees and migrants, straining resources and sparking heated political debate.
“People who are fleeing war and persecution are offered security and protection in Germany,” the minister, Thomas de Maiziere, told the newspaper Bild am Sonntag.
“But that also means that those who do not seek this protection from us are refused entry at the border.
“Anyone who doesn't want to apply for political asylum in Germany and wants to illegally enter Germany has no right to be here.”
So far this year, federal police had rejected up to 200 people a day, he said - compared to just 400 people in all of October when border controls and registration procedures buckled under a mass influx.
Those now sent back include people who want to apply for asylum in other European countries.
The ministry said that so far this year, despite winter, about 2,000 refugees had arrived every day. Police now had the capacity to register 3,500 refugees a day at the borders, the ministry said.