The likeness of Empress Josephine, born on the Caribbean island in the 18th century, was torn down from its base and crushed with sledgehammers, as seen in a photo published by the France Antilles news website.
RVN, which stands for "Red, Green, Black" after the colours of the island's unofficial flag, acted on their threat to demolish the statue in the main city of Fort-de-France after giving Mayor Didier Laguerre until Sunday to remove it.
Videos of the moment have been published on social media networks.
The demonstrators also brought down a statue to Pierre Belain d'Esnambuc, who claimed Martinique for France and established the first French town on the island in 1635.
Dozens of monuments to prominent historical figures associated with slavery have been defaced or demolished in the United States and Europe in recent weeks after the resurgence of the Black Lives Matter movement following the in-custody death of a black African American.