We evidence the importance of electron charging under nonequilibrium conditions for carbon-nanotube-based molecular bridges, using a self-consistent Green’s function method with an extended Hückel Hamiltonian and a three-dimensional Poisson solver. Our analysis demonstrates that such feature is highly dependent on the chirality of the carbon nanotube as well as on the type of the contact metal, conditioning in a nongeneralized way the system’s conduction mechanism. Based on its impact on transport, we argue that self-consistency is essential for the current-voltage calculations of semiconducting nanotubes, whereas less significant in the case of metallic ones.