The jump took SPD support to its highest in over four years. Support for Merkel's CDU and its Bavarian sister party, the CSU, fell 4 points to 33 percent - cutting the gap between the two blocs to its narrowest in records compiled by poll tracker wahlrecht.de going back to Sept 2013.
"Martin Schulz is managing above all to win back former SPD voters and to appeal to them emotionally," Emnid's Torsten Schneider-Haase told the newspaper, adding: "Such a strong shift in party preferences within a week is a one-off."
The SPD appointed Schulz, a former European Parliament president, as leader last Sunday, replacing Sigmar Gabriel who said he was standing aside to boost the party's chances.
The move has re-energised the SPD, junior partner in Merkel's 'grand coalition', ahead of September's federal election.
Schulz has vowed to unseat Merkel with a campaign aimed at overcoming "deep divisions" that he says have fuelled populism in Germany in recent years.
In a theoretical head-to-head contest for chancellor, the Emnid poll showed Merkel pipping the Social Democrat to victory with 41 percent support to his 38 percent.
The SPD has held exploratory talks with the environmentalist Greens and the far-left Linke party about forming a left-leaning coalition government after the election but they need more support if that is to become a viable option.