The violence erupted as voters sought to end a crisis which has crippled the Indian Ocean island since strongman Andry Rajoelina, 39, ousted Marc Ravalomanana four years ago.
"A district chief was killed at a polling station" in the southern town Benenitra, an interior ministry source told AFP on condition of anonymity, without giving details.
Another person was kidnapped from a voting site in Bezaha, elsewhere in the south, while a polling station was burned down in the northern district of Tsaratanana.
"There are no major problems in the voting process," the European Union's chief election observer Maria Muniz de Urquiza said five hours after polling opened.
Voters were optimistic the election would allow the country to turn the page on its political crisis which has harshly impacted the economy.
The world's fourth-largest island, the island famed for picture-perfect beaches and lemurs, is a magnet for tourists.
"I think Madagascar will emerge from the crisis in this election," said voter Alain Yves as people trickled in, voter ID cards in hand to cast their ballots in the capital Antananarivo.
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