The poll conducted by INSA for Cicero magazine asked people if they thought Merkel should run for a fourth term and 64 percent responded that she should not.
Other polling figures show that if an election were held now, Germany's two main political parties would barely scrape together 50 percent of the vote between them.
In the separate survey conducted by INSA for Bild, the Union - a combination of Merkel’s Christian Democratic Party (CDU) and Bavarian sister party the Christian Social Union (CSU) - only polled at 30.5 percent.
This number was a drop of 1.5 percent on the previous week and the lowest number ever recorded by INSA for the twin conservative parties.
With the Social Democratic Party (SPD) polling at 19.5 percent, that meant that the two parties which make up the ‘grand coalition’ which governs Germany would only win 50 percent of the vote.
This figure is a drop of 17 percent on the last national election and would have been unthinkable up until recently.
In the post-war period, the two Volksparteien (major parties) have habitually carved up the vast majority of the electorate between themselves.
Aside from the liberal Free Democratic Party (FDP), during the Cold War there was little room for other parties in national politics.
But reunification has had an effect on the political map of Germany, with first the Left Party and now the Alternative for Germany (AfD) winning large chunks of the vote in the former East.
The trend is so developed that Thuringia has had a Minister President (state governor) from the Left Party since 2014.
Meanwhile the Green Party have also managed to establish themselves in states such as the wealthy Baden-Württemberg.
In state elections in March, Baden-Württemberg became the first state in German history to give a party outside the Union and SPD the largest number of votes.
The unpopularity of the grand coalition’s refugee policy among certain sections of the populace has also affected their decline, with the AfD taking full advantage in recent elections and polling.
Things have become so bad for the SPD that rumours have been swirling in the media that their leader Sigmar Gabriel plans to stand down. Gabriel has denied the reports.
“It’s not necessarily true now that Union plus SPD means a majority in the German parliament in elections in 2017,” INSA head Hermann Binkert told Bild.
In the poll, the AfD gained support to move up to 15 percent, the Green party stayed at 13 percent, with the Left party at 10 percent.
The FDP meanwhile moved up to 8 percent, meaning they would make it past the 5 percent barrier they failed to pass to get into the last Bundestag, voted in in 2013.