We calculate the $\phi$ meson collision rate and mean free path in a hot hadronic gas. The Hidden Local Symmetry model is used to take into account interactions of $\phi$ mesons with pseudoscalar ($\pi$, $K$) and vector mesons ($\rho$, $\omega$, $K^*$, $\phi$). In contrast to previous calculations we find a significantly small mean free path (around 1~;fm at T=200MeV). This implies that $\phi$ mesons produced after hadronization in relativistic heavy ion collisions will not leave the collision region without scattering. The consequences of these findings to the analysis of $\phi$ yields are discussed.