The survey, carried out by the Emnid Institute, is a huge blow for Angela Merkel
The survey puts the centre-left Social Democrats (SPD) one point ahead of Angela Merkel's Christian Democrats (CDU/CSU).
The SPD has now gained a record-breaking 12 points since unveiling Mr Schulz as its candidate for the Chancellery last month.
The party's surge marks a humiliation blow for Merkel, who is running for her fourth term.
Political scientist Thomas Jaeger of Cologne University said: "This is a serious poll showing the SPD coming from nowhere to overtake the CDU/CSU.
"It's amazing to see how unprepared the CDU was for someone like Schulz.
"They assumed the SPD was going to stay stuck in the 20-25 percent range. They've been caught pants down."
Martin Schulz quit as European Parliament president to run for Chancellor 'MERKEL MUST GO': Brussels protest against German Chancellor Tue, February 14, 2017
Angry campaigners held placards with slogans reading 'Merkel not welcomed' and 'Merkel must go' following a spate of terror attacks against Germany.
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Protest on the sidelines of Angela Merkel's official visit in Brussels
The Emnid Institute's survey of 1,885 voters gave the SPD 33 per cent of the vote, with the CDU/CSU trailing on 32 per cent.
The SPD has been junior partner to Merkel's CDU/CSU in a grand coalition since 2013.
But ex-European Parliament chief Schulz has campaigned against many of her policies.
Merkel's party trails the SPD by one per cent, according to the poll
Martin Schulz has won back over former SPD voters – he speaks their language
Jager added: "Schulz has won back over so many former SPD voters who had turned their back on the party.
"He speaks their language and sounds like one of them.
"There's a lot of enthusiasm all of a sudden."
Finance Minister Wolfgang Schaeuble denied Merkel had been complacent
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Finance Minister Wolfgang Schaeuble, one of Merkel’s closest allies, denied the CDU/CSU had been complacent.
He said: "We're certainly taking him [Schulz] seriously. He's helped the SPD find its courage again.
"But he feels he's not a part of our grand coalition. It's a bit of a contradiction because his party has contributed to things going well in Germany."
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