Using nonequilibrium molecular dynamic simulations, the thermal conductivity of a set of Si phononic metamaterial nanowires with a twinning superlattice structure has been investigated. We first show that this latter structural modulation can yield 65% thermal-conductivity reduction compared to the straight wire case at room temperature. Second, a purely geometry-induced minimal thermal conductivity of the phononic metamaterial is observed at a specific period depending on the nanowire diameter. Mode analysis reveals that the the minimal thermal conductivity arises due to the disappearance of favored atom polarization directions. The current thermal-conductivity reduction mechanism can collaborate with the other known reduction mechanisms, such as the one related to coating, to further reduce thermal conductivity of the metamaterial. Current studies reveal that twinning superlattice nanowires could serve as a promising candidate for efficient thermoelectric conversion benefitting from the large suppression in thermal transport and without deterioration of electron-transport properties when the surface atoms are passivated.