He also refused to become the next foreign minister.
Just two days after the coalition deal was struck, Schulz announced he was abandoning his bid to serve as Germany's next foreign minister after heavy criticism from his party for seeking the job after he previously said he wouldn't serve in the next German government.
German Chancellor Angela Merkel may have given the finance ministry to her Social Democrat (SPD) coalition partners but Berlin is not putting its finances at risk, a former lawmaker told CNBC Tuesday.
Andrea Nahles, a plain-speaking 47-year-old former labor minister with a left-wing slant and strong oratory skills, will become Schulz's successor.
Many in the SPD fear that re-entering a coalition with Mrs Merkel's Christian Democrats (CDU) and the Bavarian CSU could damage the party in the long term.
This agreement reached by Mrs Merkel and the leader of the SPD Martin Schulz could be rejected by the 460,000 members of the SPD at the end of February when they vote on the alliance.
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With many SPD rank and file harboring misgivings about sharing power with Merkel again, the result of the vote, due on March 4, is wide open. "But I think the whole situation is not only bad for the SPD, it's a bad situation for all parties because people lose more and more trust in political parties".
German media report that SPD members in the state of North Rhine-Westphalia were especially opposed to Mr Schulz - formerly European Parliament president - becoming foreign minister.
The most urgent matter for the SPD is to get a new leader in place after Martin Schulz said last week he would quit to allow the party to regroup.
Germany has been without a formal government since the September 24 election and investors are anxious about a delay in policymaking, both at home and in the EU.
An INSA poll published on Tuesday showed the SPD at a record low of 16.5 percent, only 1.5 percentage points ahead of the far-right Alternative for Germany (AfD). The centre-left SPD is on course to run six ministries, including finance and foreign affairs. The party's youth wing is pushing the Social Democrats to go into opposition, and leadership questions mired its top officials.
Nahles said that she would start campaigning at the weekend for members to approve the coalition agreement with Merkel. But he changed his mind after the Union failed to form a government with two small parties.