He told German news agency, "Die Welt", that "there no statutory basis exists in the SPD's rules that allows for the appointment of a new party leader".
"Not only has a Bavarian politician passed the pinnacle of his career, but probably a woman from the north too", he added in a dig at Merkel and Horst Seehofer, leader of the arch-conservative Bavarian sister party (CSU) to Merkel's CDU.
Paul Ziemiak, leader of the conservatives' youth wing, welcomed Merkel's readiness to set out her picks for ministerial posts before a CDU party conference on February 26.
He made the decision after days of personnel debates within the SPD.
He said he hoped the party could "regain its former strength" under Nahles' leadership and as part of the German government - if members agreed to that in the upcoming ballot.
Seeking to restore order, Schulz resigned with immediate effect on Tuesday and party leaders installed Scholz as caretaker SPD chairman.
Schulz, a former European Parliament president, took over as SPD leader from Gabriel previous year, raising hopes within the party he could stand a better chance against Merkel in the September election.
"I depart this office without bitterness or resentment", he said, nearly a year after he was elected as SPD party head with 100 percent of the vote.
Schulz is expected to take a seat on the SPD's backbenches.
Schulz, 62, ditched plans to take the post of foreign minister after fierce criticism from some former allies, not least because he had pledged not to serve in a cabinet with Merkel. Media have speculated that one option might be Katarina Barley, a former SPD general secretary and family minister, or SPD veteran Thomas Oppermann.
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).
Merkel annoyed members of her Christian Democrats (CDU) by agreeing in the coalition talks to cede the finance ministry to the SPD. Merkel's conservative bloc was also down 1 point at 29.5 percent.
Similarly, the SPD regional branch in Schleswig-Holstein urged the party leadership not to nominate Nahles as leader just yet. Last Wednesday, the SPD reached an agreement with Merkel's Union in formal government coalition negotiations, a move likely to end the longest ever new government vacuum after the September 24 federal elections.