Support for her Christian Democratic Union (CDU) has dropped two percentage points to 38 percent -- its lowest since the last parliamentary election in September 2013, according to the latest weekly polls by newspaper Bild am Sonntag.
Almost one in two Germans (48 percent) believe that Merkel's decision to open the country's doors to those fleeing war was wrong. Those who back her stance stood at 39 percent.
The survey also showed political parties that have been pressing for Germany to shut its doors to refugees as gaining ground, with the far-right Alternative for Germany (AfD) and the liberal FDP both gaining one percentage point to 6 percent each.
Germany is expecting to receive between 800,000 and one million asylum seekers this year.
The record influx has left regional authorities scrambling to find ways to house the new arrivals.
Merkel has however refused to budge, insisting that Europe's largest economy can manage the large numbers.
But doubts have been growing, particularly in the southern region of Bavaria, the gateway to Germany for many of the new arrivals.
The CDU's sister party Christian Social Union (CSU) has been among the most vocal in condemning the government's refugee policy.
The CSU's president Horst Seehofer this weekend condemned what he described as Germany's "surrender" in refusing to close its borders to migrants.
He has also threatened to take the federal government to the German constitutional court, for allegedly hindering the proper functioning of regional states, some of which have been swamped by migrants and refugees.
Vice-Chancellor Sigmar Gabriel however shrugged off the threat, saying that border security was a federal, not a state matter.