"Therefore, I hereby declare that I am withdrawing my bid to enter the federal government, and sincerely hope that this would end the candidacy debate within the SPD", Schulz said in a written statement.
Seehofer is expected to give a report on the mammoth negotiations - which stretched beyond a Sunday deadline into Wednesday - to hammer out the deal to revive the so-called grand coalition that has governed Germany since 2013.
The SPD and CDU both had their worst results for decades in the election, which catapulted the far-right Alternative for Germany (AfD) into parliament for the first time, with 94 seats.
The SPD, Christian Democratic Union (CDU) and the Christian Social Union reached the coalition deal on Wednesday, which will possibly end the new government vacuum since the September 24 federal election, the longest period ever since 1949.
A Forsa poll showed nearly three-quarters of Germans thought it would be wrong for Schulz to become foreign minister, while only around a quarter thought that would be the right move.
A "no" vote would mean Germany would nearly certainly face. On Thursday night, outgoing Foreign minister Sigmar Gabriel's lashed out at the SPD leadership for having a lack of respect for party members.
Mr Schulz has confirmed he will step down as SPD leader in March and instead become foreign minister, if the coalition deal is approved by SPD members.
Kuehnert, 28, is travelling around Germany urging members to vote against the deal.
Discontent also simmered in parts of the conservative bloc on Friday.
Social Democrat won't take the job after coming under pressure over coalition deal.
Paul Ziemiak, leader of the youth sing of the CDU and Christian Social Union (CSU) said the party needed to think about who would take over from Merkel, now on the bring of a fourth term.
Merkel faced an uphill struggle to maintain power for another four years following a disastrous election campaign.
The agreement, reached after weeks of intensive talks, largely confirms the most important energy and climate policy positions of chancellor Angela Merkel's conservatives (CDU/CSU) and the Social Democrats (SPD) that emerged a few days earlier.
With a booming economy and state coffers full, Merkel can afford to buy her coalition partners' loyalty: the country's national finances will probably enjoy a surplus of €45 billion over the next four years, so spending promises can be kept while still upholding the government's determination not to borrow.