Khalfan Khamis Mohammed, serving a life sentence at the high-security prison, says the restrictions violate his civil rights.
Jeff Dorschner, a spokesman for the U.S. Attorney in Denver, did not return a phone call Wednesday seeking a response.
The story was first reported by the Denver Post.
In a handwritten filing in 2008 in Denver District Court, Mohammed said the special administrative measures that allow restrictions on federal prisoners were "in violation of the First Amendment rights, equal protection rights, cruel and unusual punishment."
Representing himself, Mohammed also complained that he was barred from watching religious programming on Arabic television, even though Christian prisoners had access to their spiritual leaders.
In her ruling Thursday, U.S. District Judge Marcia Krieger said the federal government failed to show that the people with whom Mohammed wants to communicate pose a threat to the security of the prison or the public.
The judge rejected other complaints, ruling Mohammed could not prove he has been deprived of adequate food, clothing, shelter, medical care or safety.
The federal government argued it is monitoring 20 inmates and has limited resources because many of the communications need to be translated, a claim the judge rejected.
"Simply because there is insufficient manpower to screen all mail coming into a prison does not entitle the prison to select particular inmates who cannot receive mail, or to limit the people with whom the inmates may communicate," Krieger noted.
Federal prosecutors said Mohammed remains a danger to the community because he played a crucial role in the bombing of the U.S. Embassy that killed or injured nearly 100 people.
"When it was over, (Mohammed) expressed his regret that more Americans had not died," prosecutors told the court.
Prosecutors said Mohammed has not shown the restrictions are irrational, "given that he is a convicted al-Qaida terrorist whose actions culminated in a successful strike against the United States."
Colorado's Supermax prison - short for "super-maximum security" - holds some of the country's most notorious criminals. They include Unabomber Theodore "Ted" Kaczynski and Eric Robert Rudolph, who bombed a park during the 1996 Olympics in Atlanta.