This paper analyses the notch effect in the fracture behaviour of acrylonitrile–styrene–acrylate (ASA) material manufactured by fused filament fabrication (FFF). The research is performed on 72 single-edge-notch bending (SENB) specimens containing U-notches with nominal notch radii varying from 0 mm (crack-like defects) up to 2.0 mm, and fabricated with three different raster orientations (0/90, 45/−45, 30/−60). Apparent fracture toughness values are obtained for the different conditions and the resulting notch effect is analysed through the Theory of Critical Distances. A fractographic analysis is also performed using Scanning Electron Microscopy (SEM) in order to justify the fracture (macroscopic) behaviour from the observed fracture micromechanisms. The notch effect observed in the three ASA raster orientations is very similar, and lower than that observed in other FFF polymeric alternatives (ABS, PLA).