The Court of Appeals concluded that the order does not raise "substantial" constitutional issues that would warrant an immediate intervention.
The decision is the latest legal setback for the Republican former president, who has repeatedly railed against a gag order that prevents him from commenting on witnesses, jurors and others who were involved in the case.
But it could be short lived.
The trial judge, Juan Merchan, is expected to rule soon on a defence request to lift the gag order.
Trump campaign spokesman Steven Cheung said on Tuesday the ex-president's legal team would "continue to fight against the unconstitutional gag order imposed by Justice Merchan".
Trump's lawyers filed a notice of appeal with the state's high court on May 15, during the former president's landmark criminal trial.
They argued that the gag order restricted Trump's "core political speech on matters of central importance at the height of his presidential campaign".
But the Court of Appeals disagreed.
In a decision list posted on Tuesday, the court said it would not automatically hear the case, writing that "no substantial constitutional question is directly involved".
Trump's lawyers were essentially seeking a shortcut to expedite their appeal, which was rejected by the state's mid-level appeals court last month.
They have 30 days to file a motion for leave to appeal, according to court spokesman Gary Spencer.
Merchan imposed the gag order on March 26, a few weeks before the start of the trial, after prosecutors raised concerns about the presumptive Republican presidential nominee's tendency to criticise people involved in his cases.
During the trial, Merchan held Trump in contempt of court and fined him $US10,000 ($A15,000) for violating the gag order.
The judge threatened to put Trump in jail if he did it again.
The order remains in effect weeks after the conclusion of the trial, which ended with Trump's conviction on 34 counts of falsifying business records arising from what prosecutors said was an attempt to cover up a hush money payment to porn actor Stormy Daniels just before the 2016 election.
Daniels claims she had a sexual encounter with Trump a decade earlier, which he denies.
He is scheduled to be sentenced on July 11.
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