In the latest "Deutschlandtrend" survey commissioned by public broadcaster ARD, 51 percent of people said they were afraid because of the large numbers of refugees arriving compared with 47 percent saying they were unafraid.
The previous poll, just three weeks ago, put that same number at 38 percent.
The turn in the polls has been reflected in changing rhetoric from mainstream politicians, with Vice-Chancellor Sigmar Gabriel telling Der Spiegel on Friday that "we are quickly hitting the limits of our capabilities in Germany."
While there was no legal limit to the number of asylum seekers Germany might host, Gabriel said, "there are practical limits to the capacity of local communities".
Refugees hit Merkel popularity
Arrivals sped up following Merkel's decision to allow Syrian refugees stuck in Hungary into Germany, rather than forcing them to remain in the first EU country where they set foot as the so-called Dublin regulations require.
In September alone, 160,000 refugees were registered for the first time in Germany, although the actual number arriving is likely to be significantly larger.
The Chancellor's approval rating sink nine points over the last month, to 54 percent.
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 percent.
Less than half of respondents - 48 percent - said they were satisfied with Merkel's government, down five points.
New workers needed to fill jobs
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A majority of the people surveyed – 58 percent – continue to believe that refugees are needed to shore up the German labour market, which is struggling with a lack of skilled workers.
That compared with 39 percent of people who thought that the number of refugees arriving was so large as to threaten Germany's prosperity.
Pollsters surveyed 1001 eligible voters on September 28th and 29th by telephone.