An analytical derivation is presented for computing mass-loss rates of Cepheids by using the method of Castor, Abbott, and Klein modified to include a term for momentum input from pulsation and shocks generated in the atmosphere. Using this derivation, mass-loss rates of Cepheids are determined as a function of stellar parameters. When applied to a set of known Cepheids, the calculated mass-loss rates range from 10-10 to 10-7 M☉ yr-1, larger than if the winds were driven by radiation alone. Infrared excesses based on the predicted mass-loss rates are compared to observations from optical interferometry and IRAS, and predictions are made for Spitzer observations. The mass-loss rates are consistent with the observations, within the uncertainties of each. The rate of period change of Cepheids is discussed and shown to relate to mass loss, albeit the dependence is very weak. There is also a correlation between the large mass-loss rates and the Cepheids with slowest absolute rate of period change due to evolution through the instability strip. The enhanced mass loss helps illuminate the issue of infrared excess and the mass discrepancy found in Cepheids.