The behavior of a small isolated hydrate-free inclusion (a gas bubble) within a porous matrix filled with methane hydrate and either water or methane gas is analyzed. Simplifying assumptions of spherical symmetry, an infinite uniform porous medium, and negligible effects of background temperature and pressure variations focus the investigation on the features of the dynamics of a single bubble determined by a phase transition. Two solutions are presented: an exact solution of the Stefan problem obtained when the effects of gas and water flow are neglected, and a numerical solution of the full problem. The solutions are in good agreement with each other and with known asymptotic dependencies, confirming that the effects of inertia and convection transport can be neglected in the case of small inclusions. It is found that, after an initial adjustment, the radius of any small bubble decreases with time following a self-similar solution of the Stefan problem. The lifetime of a bubble is evaluated as a function of initial radius and the system's physical parameters. Possible effects of such inclusions on the filtration of methane to the surface and other aspects of the dynamics of hydrate-bearing deposits are discussed.