The aim of this work is to develop a single‐step process to produce hydroxyapatite/polycaprolactone (HAp/PCL) composite filaments for 3D printing of bone scaffolds by fused deposition modeling (FDM). The HAp/PCL composite filaments are produced by hot‐melt extrusion, with direct in situ blending. For practical purposes, the effect of PCL particle size on filament homogeneity and printability is assessed between PCL in powder and pellet form. The effect of HAp content on processing parameters and filament properties is also evaluated. Filament extrudability, homogeneity, and shape consistency improve with increasing HAp content up to a threshold of 40 wt%. Furthermore, an optimal range of the composite melt viscosity for the extrusion process is defined. The produced filaments are successfully 3D printed by FDM and the resulting prototypes show improved compressive modulus and degradation rate with increasing HAp content. A cytocompatibility assay is conducted, which suggests an optimal HAp content to be less than 40 wt% in terms of cell viability, adhesion, and proliferation. The developed method offers several advantages, as it completely avoids the use of toxic solvents and enables the incorporation of very high HAp concentrations, further improving the chances of implementation of FDM for bone tissue regeneration medicine.