Methyl iodide is trapped as the monomer and as clusters in the parahydrogen, known as a quantum crystal, at temperatures below about 8 K. UV illumination of the deposited sample at about 5 K causes the dispersal of clusters and the production of the methyl radical, methane, and ethane as evidenced by their infrared absorption spectra. Thermal annealing of the photolyzed sample at temperatures up to 11 K results in the disappearance of the methyl radical, the enhancement of ethane, and the regeneration of methyl iodide. When the initial concentration of the iodide is small, the clusters in the deposited sample are suppressed. For such a sample the UV excitation produces the methyl radical and methane but the formation of ethane is negligibly small. Relevance of the present work to studies of photolysis in gaseous clusters of methyl iodide is discussed.