The INSA poll for German daily Bild showed support for the AfD, which was dogged by infighting in the first half of the year and saw its founder break away to form a new party, climbing to 5.5 percent, its highest level since late May.
The survey also showed support for German Chancellor Angela Merkel's conservative bloc slipping 1.5 points to 40 percent, still the strongest party by far, but its lowest reading since late June.
Merkel was feted in Germany earlier this month for opening Germany's borders to refugees fleeing war in Syria, Afghanistan and Iraq, but has since backtracked amid an outcry from the leaders of Germany's 16 federal states.
"The refugee crisis is pulling the conservatives down and pushing the AfD over the 5 percent threshold," INSA head Hermann Binkert told Bild.
Presenting its asylum policy at a news conference in Berlin last Monday, the AfD backed the introduction of border controls to stem the tide of refugees entering Germany from Hungary, via Austria.
Over the weekend, Merkel bowed to pressure from state premiers, including Bavarian leader Horst Seehofer, and agreed to such controls.
Bernd Lucke, an economics professor who founded the AfD in 2013 primarily as a platform for opposing euro zone bailouts, was ousted as leader of the party in early July after a bitter public row with leaders of the AfD's east German wing.
Frauke Petry, a 40-year-old former chemist and businesswoman who led the AfD's successful run in three eastern state elections last year by espousing a tough line on immigration and virtually ignoring euro zone issues, now runs the party.
Lucke, decrying a xenophobic shift in the AfD, has since left and founded a new party, the Alliance for Progress and Renewal (ALFA).
As if by design? 'Divide and conquer', somethings never change, and the real 'war' is always within, on your own servants or citizens if we want to be PC.