The analytical solution of the associative mean spherical approximation (AMSA) for a Yukawa dimerizing multicomponent hard-sphere fluid is derived. The general multi-Yukawa case is discussed. The simpler one-Yukawa case with factorizable coefficients is explicitly solved. As in the previously discussed electrolyte case the solution of the AMSA reduces to the solution of only one nonlinear algebraic equation for the scaling parameter Gamma(B). The analytical results for the AMSA closure is illustrated by numerical examples and computer simulation for the one-component one-Yukawa dimerizing fluid. Good agreement between theoretical and computer simulation results was found for both the thermodynamic properties and the structure of the system.