We present a microscopic theory for dynamic friction on an intramolecular vibrational coordinate of a diatomic molecule dissolved in a simple liquid. Previous theoretical approaches to calculating dynamic friction have either used molecular hydrodynamics or employed a concept of instantaneous normal modes. Both methods have their limitations: molecular hydrodynamics is unable to correctly describe the dynamics on short time or length scales, while the instantaneous normal modes approach can be expected to work at short times only. We apply the theoretical formalism developed by us earlier to describe self-diffusion in liquids [M. Vergeles and G. Szamel, J. Chem. Phys. 110, 3009 (1999)] to the calculation of dynamic friction. We begin by deriving an equation of motion for the phase space probability distribution of the diatomic molecule. From it we obtain an equation for the bond velocity autocorrelation function. This equation has the same form as the one obtained from the generalized Langevin equation, which allows us to identify the dynamic friction kernel. Our predictions quantitatively agree with the results of molecular dynamics (MD) simulations.