In August, around 4,200 migrants crossed into Germany, down from around 4,550 in July and a tiny fraction of the 64,700 migrants registered in January, the spokeswoman said.
The police data is based on checks in border areas. Figures for how many people registered in reception centres in August, which are usually higher, are due to be released next week.
Germany took in hundreds of thousands of migrants last year, mainly people fleeing conflicts in Syria, Iraq and Afghanistan.
The inflows have fallen sharply since early this year due to border closures in southeastern Europe and an EU-Turkey accord. Under that deal, Ankara has agreed to take back migrants leaving its shores for Greece in return for visa-free travel in Europe for its citizens, financial aid and an acceleration of Turkeys EU accession talks.
German Chancellor Angela Merkel has faced growing criticism for her open-door refugee policy, Reuters reported.
In a significant change of tone this week, she stressed the need to accelerate the deportation of foreigners who have been denied asylum, in response to rising public concerns.