The theater said Maximova died at home and no cause of death was immediately determined. She had been working as a ballet coach and was not known to be suffering from ill health.
Ballet directors and President Dmitry Medvedev praised Maximova's work as an artist and a teacher of young ballerinas, and mourned her death as a great loss to Russia.
Maximova's dancing career at the Bolshoi spanned three decades, from her debut as Masha in "The Nutcracker" in 1958 until 1988. Called "Ekaterina the Great," or Catherine the Great, for her impeccable technique and versatility, she danced most of the major female roles of classical ballet and also experimented with avant-garde dance.
Her partner on the stage and in life was her husband Vladimir Vasiliev, who following his dancing career served for five years as artistic director of the Bolshoi.
Bolshoi ballet master Boris Akimov said he was shaken by the unexpected death of Maximova, who had participated in a meeting of the troupe's ballet coaches on Sunday.
"She was full of energy and enthusiasm," Akimov said. "She was happy and active and made many serious, sensible artistic suggestions. And in the evening she was at her beloved ballet 'Spartacus,' where for many years she shone in the main female role."
Andrei Petrov, the artistic director of the Kremlin Ballet, where Maximova also had coached dancers since 1990, said she would be badly missed.
"She was a great ballerina, a teacher from God, and at the same time she was always able to speak the truth no matter how bitter it might be," Petrov told the news agency.
Medvedev sent his condolences to Maximova's family, friends and co-workers.
"You lost someone near and dear, but Russian art has lost a great ballerina, whose rare multifaceted talent is rightfully deemed to belong to world culture," Medvedev wrote in a telegram, the Kremlin said. "With her brilliant dancing, astonishing grace and beauty she literally charmed audiences."
Maximova is survived by her husband and mother.