The shock findings come despite the number of newcomers into the country falling significantly on the year after the open-door approach of 2016.
A record 890,000 mainly Muslim migrants from the Middle East, Africa and elsewhere arrived in Europe’s largest economy in 2015, prompting concerns about security and integration.
Arrivals have slowed this year, with the Federal Office for Migration and Refugees (BAMF) saying on Friday around 305,000 new asylum seekers were registered during the first 11 months of 2016.
The BAMF received 26,438 asylum applications in November – a fall of around 54 per cent on the year.
However, a survey by pollster Forschungsgruppe Wahlen for broadcaster ZDF found 58 per cent of Germans see refugees and integration as the most important problems Germany is facing.
Chancellor Angela Merkel’s popularity has waned since migrants started arriving in large numbers last summer and she expects next year’s federal election, in which she plans to run for a fourth term, to be “tough like no other”.