Chairman of the German Police Union (DpolG) Rainer Wendt told the Welt am Sonntag newspaper that Germany should build a fence along its border with Austria.
"If we close our borders this way, Austria will also close its border with Slovenia, and that's exactly the effect we need," he said, insisting that Germany could no longer send out the message that everyone was welcome.
"Our internal order is in danger, we are close to social unrest, someone has to pull the emergency brake now," he said, stressing that the only person who could do so was Chancellor Angela Merkel.
Merkel's spokesperson Steffen Seibert said on Monday that the Chancellor believed a fence would not do much to stop desperate people from entering the country.
The deputy president of police union GdP criticized Wendt's plan, saying that Wendt offered "no contribution to solving the problem", according to Frankfurter Allgemeine Zeitung.
"The past has shown that border fences do not stop refugees, as authorities have also seen in Hungary," said GdP's Jörg Radek.
"A flood of refugees behaves in physics like water: they look for another way in."
"The Schengen agreement is such a great boon to Europe that for me it is completely unimaginable that we would actually shut off our borders, as suggested by the union," Dreyer said on Sunday.
Wendt had previously called for the reintroduction of internal European border controls and demanded more personnel to deal with a record flood of refugees.
Europe has abolished passport controls between 26 countries in the so-called Schengen zone, which incorporates 26 EU members and stretches from Spain to Finland, and also includes Switzerland, Norway, Iceland and Liechtenstein.
However, police have stepped up spot-checks of travellers on intra-European trains, highways and flights.
Dreyer said that Wendt's most recent suggestions run “completely and totally” contrary to European ideals.