Chief Justice Ronald Moon said the editorial, which accused the court of ducking the issue, contained "self-serving, intemperate accusations and uninformed remarks."
The paper published Moon's letter criticizing the editorial.
Advertiser editor Gerry Keir had no comment.
The high court recently issued an order that no names of police officers be made public until the year-old legal case goes through trial and the appeals process.
The case seeking to make the names of disciplined officers public was brought in 1993 by the University of Hawaii chapter of the Society of Professional Journalists.
Other news organizations have joined as plaintiffs.
It is being opposed by the State of Hawaii Organization of Police, which represents city and county police in collective bargaining.
The high court had disagreed with a lower court's rejection of the police union's motion to keep the names secret.
It said release of the names could lead to the loss of what the court called the officers' "vital rights."
The October Advertiser editorial said, "This non-decision smells of a court acting out of fear of antagonizing the losing side, one of the worst motivations for any jurist."
Moon called the editorial "accusatorial, libelous and misleading.
"It is entirely reprehensible and irresponsible of you to accuse the court of 'acting out of fear of antagonizing the losing side,' particularly where your newspaper is a party to the case," Moon wrote.
He noted that the case didn't come to the Supreme Court on appeal but by way of a petition for a writ of mandamus which involved the limited issue of releasing the names before the trial and appeals process.
If the case returns to the Supreme Court after the trial, the court will have a full evidentiary record to consider and not just the selected materials submitted by the parties in the mandamus proceeding, Moon said.
"You are aware that courts must act on the basis of the evidence and the law," he said, "not on the basis of who will be angered by the result ? whether the police, the newspapers or others."
By: Editorial Staff HAWAII'S CHIEF JUSTICE has demanded an apology from the Honolulu Advertiser for an editorial that criticized the court for agreeing to keep secret the names of disciplined police officers.