The poll published on Friday by ZDF Politbarometer put support for the Greens at 24%, up from the 14.8% they scored in the federal election in September, while the SPD had 22%, down from around 26% it gained in September.
The poll showed former Chancellor Angela Merkel's conservatives, who won two regional elections this month, were the strongest party, with 26%.
Friday's survey, along with the SPD losing an election on Sunday in North Rhine-Westphalia (NRW), Germany's most populous state, heap pressure on the chancellor after just five months in office.
The rise of the Greens, who were the kingmakers in federal coalition talks, is partly due to the popularity of former party leaders Robert Habeck and Annalena Baerbock, who came first and second in voters' assessment of German politicians.
Around 74% of the survey takers were satisfied with Baerbock's work as foreign minister on the Ukraine crisis, while 67% thought that Habeck, the economy minister, was doing a good job.
Scholz, who heads the coalition with the Greens and the FDP liberals, came in third place, the survey showed, with only half of poll takers assessing his response to the Ukraine war as positive.
Scholz pivoted to a more assertive foreign policy when the Ukraine crisis erupted, announcing a dramatic hike in military spending.
But he faced criticism this month at home and abroad, including from members of his coalition's junior partners, that Germany was failing to lead Western efforts to supply Ukraine with heavy weapons.
Some 58% of German are in favour of sending heavy weapons, while 34% are against it, the survey found.
The Greens campaign in the federal election focused on a transition to more renewable energy, now seen as more urgent as Germany tries to cut dependence on Russian fossil fuels. Some 64% of respondents in the survey thought expansion of renewables was going too slowly.
The poll surveyed 1,162 people from May 17-19.
(Reporting by Riham Alkousaa; Editing by Miranda Murray and Frances Kerry)
