This study presents a method to melt-spun biocompatible composite fibres from poly(lactic acid) (PLA) and nano-sized hydroxyapatite (HAp) particles. Different loading concentrations of HAp particles in the PLA fibres and solid-state draw-ratios (SSDR) were evaluated in order to study their influence on the mechanical, thermal and morphological properties. The results showed that the incorporation of the HAp particles was homogeneously distributed in the PLA fibres towards their surface and that the SSDR played an important role in order to improve the mechanical properties. The melt-spun PLA/HAp composite fibres, produced in this study, had also the potential to be processed into a fibrous scaffold, which was demonstrated by a 3D woven structure.