The actress died of complications from a heart attack, son Jod Kaftan told CNN.
Martel played a diverse range of characters during the 1960s, and was known as "The Chameleon" by Hollywood casting directors due to her ethnic ambiguity.
She had roles in The Monkees, I Dream of Jeannie, Hogan's Heroes and Gunsmoke.
Perhaps her most iconic role was as T'Pring, a Vulcan princess in Star Trek.
Leonard Nimoy, who played Spock in the series, took to Twitter to express sadness upon learning of Martel's death Tuesday.
Saying goodbye to T'Pring, Arlene Martel. A lovely talent.— Leonard Nimoy (@TheRealNimoy) August 13, 2014