Court records showed defendant Harrison Floyd was due to appear in court on Friday morning but Judge Scott McAfee told reporters he would not appear after all.
McAfee said court records contained "misinformation" about Floyd's case.
"Mr. Floyd is entitled to a first appearance... one will not be happening today here," he told reporters.
It was not clear what would have been discussed in Floyd's hearing but initial appearances typically address the terms of possible bond and conditions of release before trial.
All 18 other defendants in the case have been released after posting bond, records show.
Bail amounts range from $US200,000 ($A312,000) for Trump to $US150,000 for former New York mayor Rudolph Giuliani to $US10,000 for Misty Hampton, a former election supervisor in a rural Georgia county who is accused of tampering with voting equipment.
Floyd, a former US Marine and mixed martial arts fighter, is accused of participating in a scheme to pressure an election worker to falsely admit to voting fraud.
In a separate case, he was arrested in Maryland in May and charged with assaulting FBI agents who tried to serve him with a subpoena, court records show.
It was not clear on Friday whether Floyd, who headed a group called Black Voices for Trump, had been denied bond or was unable to come up with the money needed to secure his freedom before trial.
For now, he will remain in Fulton County Jail, which is being investigated by the US Department of Justice for violence and unsanitary conditions, as well as 15 inmate deaths last year.
One of those was a man whose family says in a lawsuit was "eaten alive" by bedbugs.
Floyd's non-appearance comes after a momentous day in which Trump's mug shot from the jail was released.
Trump, 77, was captured glaring at the camera in the first such photograph of a former president in US history, yet another extraordinary moment for the front-runner for the 2024 Republican nomination.
Fulton County District Attorney Fani Willis has charged Trump with 13 felony counts including racketeering for pressuring state officials to reverse his 2020 election loss and setting up an illegitimate slate of electors to undermine the formal congressional certification of Democratic President Joe Biden's victory.
After spending about 20 minutes at the jail on Thursday evening, Trump repeated the claim that Willis' prosecution - along with the others he faces - is politically motivated.
"What has taken place here is a travesty of justice," he told reporters.
"I did nothing wrong, and everybody knows it."
One of the final defendants to surrender, former Justice Department official Jeffrey Clark, turned himself in early on Friday and was released on $US100,000 bond, records show.
Trump has not yet entered a plea in the Georgia case.
He has pleaded not guilty in two federal cases accusing him of seeking to overturn the 2020 election and retaining classified documents after leaving office, and to a New York state case linked to hush money payments to a porn star.
Far from damaging his candidacy for the Republican Party nomination, however, the four cases filed against him have only bolstered his standing.
He holds a commanding polling lead in the Republican race to challenge Biden in the November 2024 election.
