Molecular dynamics calculations based on rigid molecules have been used to study the solvation structure and dynamics of an azide ion in methanol and water. The ion is found to have either five to six methanols or six to seven waters in its solvation cage. The calculated reorientation time, T(R), is longer in methanol than in water by a factor of two to three and is sensitive to the assumed charge distribution of the ion. The results of the simulations are discussed in the light of recent measurements of T(R) and of the energy relaxation and dephasing times for the asymmetric stretching vibration of N3- in protic solvents.