Femtosecond time-resolved x-ray diffraction is used to study a photoinduced phase transition between two charge density wave (CDW) states in 1T-TaS₂, namely the nearly commensurate (NC) and the incommensurate (I) CDW states. Structural modulations associated with the NC-CDW order are found to disappear within 400 fs. The photoinduced I-CDW phase then develops through a nucleation and growth process which ends 100 ps after laser excitation. We demonstrate that the newly formed I-CDW phase is fragmented into several nanometric domains that are growing through a coarsening process. The coarsening dynamics is found to follow the universal Lifshitz-Allen-Cahn growth law, which describes the ordering kinetics in systems exhibiting a nonconservative order parameter.