Miami-Dade County Judge William Altfield said two of the five unreleased video clips depict the singer's genitalia during a urine test for drugs at the Miami Beach Police Department.
He agreed with lawyers for Bieber, who turned 20 on Saturday, that airing the videos would be an invasion of privacy that outweighed the public's right to know.
"Mr Bieber's right to privacy is paramount," the judge said. "He has not lost his right to privacy, and that is what is important here."
Lawyers for news outlets had previously suggested any sensitive portions be blacked out and the rest released under Florida's liberal open records laws.
Much of the footage was released last week, some of it showing Bieber walking unsteadily during a sobriety test.
Bieber has pleaded not guilty to charges of driving under the influence, resisting arrest and driving with an expired licence.
He and R&B singer Khalil Amir Sharieff were arrested early on January 23 during what police called an illegal street drag race between a Lamborghini and a Ferrari. Neither has been charged with drag racing.
Bieber's lawyer Roy Black said he was satisfied with the ruling. He said the three clips to be released without redaction are shot from an angle that is too far away to discern what is going on.
Prosecutors said they will release all five remaining clips in a few days, after the court-ordered redactions are completed.
Evidence released previously showed that a breath test found Bieber's blood-alcohol level below the .02 threshold considered intoxicated for under-age drivers.
The urine test found the presence of the active ingredient in marijuana and the antianxiety drug Xanax. Bieber told officers he had been smoking marijuana before his arrest, according to police reports.
A trial date has not been set.