Danish PM Lars Lokke Rasmussen said the decision was “not a happy moment” but Denmark “must respond” to Sweden’s restrictions.
Danish police will carry out border spot checks for the next 10 days.
The two countries are the latest to impose controls in Europe’s Schengen passport-free travel area.
In a letter to the European Commission, Inger Stojberg, Denmark’s integration minister, said the controls would focus initially on the border with Germany but may be extended to all of Denmark’s borders.
Inger Stojberg said the measures taken by Sweden meant Denmark was “faced with a serious risk to public order and internal security because a very large number of illegal immigrants may be stranded in the Copenhagen area”.
The new controls would not cause a problem for “ordinary” Danes and Germans, Lokke Rasmussen said.
“We are introducing temporary border controls, but in a balanced way,” the prime minister said.
“If the European Union cannot protect the external border you will see more and more countries forced to introduce temporary border controls.”
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