Biological self-assembly is a fundamental aspect in the development of complex structures in nature. A paradigm for such a process is the assembly of tobacco mosaic virus (TMV) capsid proteins into helical rods around the viral genome. The self-assembly process of the virus is typically modelled through attractive interactions between protein subunits, however capsid proteins also interact with their aqueous environment through solvation free energy. An open question is what role solvation plays in virus self-assembly. Here, we show that a purely geometric model of nonpolar solvation free energy, the morphometric approach, is sufficient to simulate the assembly of up to three protein subunits of TMV. The lowest solvation free energy states we find in a geometric simulation setting are remarkably close to the correctly assembled states of various experimentally determined structures. This demonstrates that van der Waals forces and entropic considerations are sufficient to guide assembly in the absence of attractive interactions between protein subunits. It further illustrates the impact of the morphometric approach as a computationally efficient model for nonpolar solvation free energy of solutes, in particular those with complicated geometry. This demonstration of the role of solvation raises important questions about the driving forces behind biological self-assembly and the paramount role of geometry.