The forces acting on solar Coronal Mass Ejections (CMEs) in the interplanetary medium have been evaluated so far in terms of an empirical drag coefficient $C_{rm D} sim 1$ that quantifies the role of the aerodynamic drag experienced by a typical CME due to its interaction with the ambient solar wind. We use a microphysical prescription for viscosity in the turbulent solar wind to obtain an analytical model for the drag coefficient $C_{rm D}$. This is the first physical characterization of the aerodynamic drag experienced by CMEs. We use this physically motivated prescription for $C_{rm D}$ in a simple, 1D model for CME propagation to obtain velocity profiles and travel times that agree well with observations of deceleration experienced by fast CMEs.