The new members of the National Assembly will be tasked with choosing a successor to 86-year-old President Raul Castro when he steps down next month.
As voting was about to begin, however, the foreign ministry issued a statement insisting that even without a Castro as president the Cuban revolution they led will endure into the next generation.
"Some hear siren songs and announce the end of the 'Castro era,'" it said on Twitter. "The next president will not have that surname. But without a doubt, it will be a son of the Revolution."
Raul took over in 2006 from his ailing brother Fidel, who had governed since seizing power during the 1959 revolution.
Eight million Cubans are expected to turn out to ratify 605 candidates for an equal number of seats in the Assembly, a process shorn of suspense and unique to the Communist-run Caribbean island nation.
"They're the most important elections of recent years, because we are going to vote for new people who will govern from then on," day-care center guardian Ramon Perez told AFP.
Today's general election is the first since the death in 2016 of Fidel Castro, and marks the beginning of major change at the top in Cuba.
Candidates may be either members of the Cuban Communist Party or not, and may also belong to trade unions or be students.
"The designation of candidates is based on merit, abilities and the commitment of the people," Raul Castro said when he announced the elections last year.
"Nobody exchanges promises for votes, or boasts of his abilities to get supporters... This is the true and exceptional face of what we proudly call socialist democracy," the official daily Granma wrote.
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