Two months after an election drubbing, the SPD scored 19 percent in the survey conducted by the Forsa institute - the lowest mark since the organisation began polling.
In Germany's September 27 election that propelled Merkel to a second four-year term, the SPD captured 23 percent of the vote, its worst result in modern history.
The party has since installed a new leader, Sigmar Gabriel, and pledged a new beginning in opposition after 11 years in power.
Profiting from the SPD's agony are the environmentalist Green party, which gained a percentage point to 13 percent, and Merkel's centre-right Christian Democrats, which also rose by one point to 37 percent.
The pro-business Free Democrats, Merkel's new coalition partners, however, lost a percentage point, slipping to 12 percent.
Forsa interviewed around 2,500 people for the poll, published by the RTL television channel and Stern magazine.