Ms Nichols broke barriers in her role as Lieutenant Nyota Uhura in the series, becoming one of the first black actresses in the US to play a figure in authority.
She was later employed by Nasa in an effort to encourage more women and African-Americans to become astronauts.
She died of natural causes on Saturday night, her son Kyle Johnson said.
In a statement posted on Facebook, Mr Johnson wrote: "I regret to inform you that a great light in the firmament no longer shines for us as it has for so many years.
