Biodegradable materials in the form of fibres and yarns have attracted increasing attention due to a large surface area and various geometric possibilities in three-dimensional polymeric scaffolds for tissue engineering applications. In this study, poly(lactic acid) fibres were produced by melt spinning and subsequent solid-state drawing in order to serve as matrix materials for fibre-based scaffold architectures. The processing of both monofilament and multifilament fibres as well as draw ratios and temperatures were investigated to analyze the effect of process variables on the properties. Two different polylactides with different molecular weight were studied and characterized in terms of their tensile and thermal properties and morphology. The relevance of fibre formation, solid-state drawing and drawing temperatures was clearly supported by the results, and it was shown that the physical properties, such as crystallinity, mechanical strength and ductility can be controlled largely by the drawing process. The obtained fibres demonstrated great potential to be further processed into biotextiles (woven, knitted, or nonwoven scaffolds) using the textile technologies.