New biodegradable and biocompatible composites are continuously developed for biomedical applications (e.g., from drug delivery devices to tissue engineering scaffolds). Properties of such systems may depend on their morphology and structure, which are attained after their processing, and therefore, the study of the crystallization kinetics has a particular relevance. The crystallization kinetics of hydroxyapatite-filled poly(butylene terephthalate-co-alkylene dicarboxylate)s has been studied under non-isothermal conditions, using a wide range of cooling rates and different kinetic models. Based on our results, nanohydroxyapatite (nHAp) particles were found to effectively act as additional nucleation sites for poly(butylene terephthalate-co-succinate) (PBST), giving rise to an increased crystallization rate with respect to pure PBST. However, the overall growth rate of HAp nanocomposites decreased compared to the corresponding homopolymers with longer aliphatic dicarboxylic acids (i.e., adipic and sebacic acid derivatives). In order to clarify this point, the activation energy for non-isothermal crystallization was evaluated using the Friedman method and significant differences were observed, suggesting a disturbing effect of nanoparticles on the motion of molecular chains that hindered their capability to reach the growing crystallization front. Isoconversional methods provided a good understanding of the kinetics of the crystallization process and significant information regarding the activation energy, relative crystallinity, and global and local Avrami exponents.