Manzarek formed the group - whose worldwide hits included "Light My Fire" and "L.A. Woman" - with Jim Morrison in 1965 after the two met by chance in Venice Beach, California.
He died surrounded by his wife Dorothy and brothers Rick and James in a clinic in Rosenheim in Bavaria after "a lengthy battle with bile duct cancer," said a statement on the Doors Facebook page.
"I was deeply saddened to hear about the passing of my friend and bandmate Ray Manzarek today," The Doors' guitarist and long-time collaborator Robby Krieger was quoted as saying.
"I'm just glad to have been able to have played Doors songs with him for the last decade. Ray was a huge part of my life and I will always miss him," he added.
Tom Vitorino, the keyboardist's manager, told news agency AFP: "Ray Manzarek was larger than life. He will be missed."
The Doors were one of the biggest acts of the 1960s, selling over 100 million albums worldwide and earning 19 Gold, 14 Platinum and five multi-Platinum albums in America alone.
Morrison impressed Manzarek, who moved from Chicago to Los Angeles to study film, with an early version of "Moonlight Drive" during their chance meeting on Venice Beach.
Manzarak was responsible for the band's trademark sound, including the rolling organ on songs like "Light My Fire." Other hits included "Break On Through to the Other Side," "The End" and "Hello, I Love You."
He was "really the driving force behind (the band) to make it all happen," former band manager Bill Siddons said. "He was the guy behind the curtain that made things happen."
Morrison's untimely death in 1971 aged 27 effectively ended the band's iconic phase, although the group continued to perform and release music with various band line-ups.
Manzarek wrote a best-selling book about his life, "Light My Fire: My Life with The Doors," in 1998. He was played by Kyle McLachlan in the 1991 Oliver Stone biopic "The Doors."
Slash, the former lead guitarist of Guns N' Roses, was among the first to pay tribute, posting on his Twitter account: "RIP Ray Manzarek words cannot express."
Morrison's sudden death - he was found in a bathtub in his Paris apartment - stunned fans of the band, which broke fresh ground in psychedelic rock with such hits as "Riders on the Storm" and "People are Strange" and "Light My Fire".
There was never an autopsy, giving rise to multiple conspiracy theories, as Morrison's remains were buried in the French capital's Pere Lachaise cemetery, alongside other such notables as Marcel Proust, Gertrude Stein and Oscar Wilde.
Morrison moved to Paris after the 1971 release of "L.A. Woman" and lived in the then-not-yet-hip Marais district with partner Pamela Coulson. It was she who found him dead, with a heart attack officially cited as the cause.
Manzarek, who did much to keep the Doors flame burning, once suggested another possibility. Recalling a 1970 conversation with Morrison, he wondered if the intense frontman had just faked his death to start a new life incognito.
In 2011 Manzarek and Krieger marked the 40th anniversary of the singer's death with a sell-out concert at the Bataclan club in Paris.
The Doors were inducted into the Rock and Roll Hall of Fame in 1993 and have a star on the Hollywood Walk of Fame, where flowers were placed Monday in Manzarek's memory.