Talon, 67, is due to step down next year after completing his second term in office, with elections scheduled for April.
A businessman known as the “king of cotton”, he first came to power in an election in 2016. He had promised not to seek a third term and had already named a successor.
The French Embassy has urged its citizens to stay indoors for their safety.
Benin has been regarded as one of Africa’s more stable democracies. It is the continent’s largest cotton producers, but ranks among the world’s poorest countries.
This apparent coup in Benin comes just over a week after Umaro Sissoco Embaló was overthrown as president in nearby Guinea-Bissau.
In recent years, there have been several coups in West Africa, including in Burkina Faso, Guinea, Mali and Niger, heightening fears that the security of the region could worsen.
Benin has seen a rise in jihadist activity in recent years, as groups linked to Islamic State and al-Qaeda spread to the south.