More than half — 51 per cent — of respondents said the arrival of so many newcomers at once made them fearful, according to the survey for public broadcaster ARD.
The result marked a 13-point rise compared to early September, a month in which 280,000 migrants crossed the border into Germany — more than in all of 2014.
Forty-seven per cent said they were not afraid of these developments.
Merkel, who has attempted to rally Germans to the task of welcoming hundreds of thousands of people fleeing war and persecution, saw her approval rating sink nine points over the last month, to 54 per cent.
Meanwhile support for the chief critic of her asylum policies from her own conservative camp, Bavarian state premier Horst Seehofer, surged 11 points to 39 per cent.
Less than half of respondents — 48 per cent — said they were satisfied with Merkel’s government, down five points.
Berlin is now stepping up action to deter economic migrants from trying to obtain asylum in the country, in a bid to free up resources to deal with applicants from war-torn countries like Syria.
On Tuesday, the government said it would add Albania, Kosovo and Montenegro to a list of so-called safe origin countries, which would result in swifter deportations of migrants from these states.
Vice Chancellor Sigmar Gabriel admitted that many towns and cities were already overwhelmed by the task of housing migrants.
“We are quickly hitting the limits of our capabilities in Germany,” he told news website Spiegel Online.
Gabriel noted that there was no upper limit for the number of asylum-seekers under German law but there are practical limits to the capacity of local communities. — AFP