In many contexts, animals assess each other using signals that vary continuously across individuals and, on average, reflect variation in the quality of the signaller1,2. It is often assumed that signal receivers perceive and respond continuously to continuous variation in the signal2. Alternatively, perception and response may be discontinuous3, owing to limitations in discrimination, categorization or both. Discrimination is the ability to tell two stimuli apart (for example, whether one can tell apart colours close to each other in hue). Categorization concerns whether stimuli are grouped based on similarities (for example, identifying colours with qualitative similarities in hue as similar even if they can be distinguished)4. Categorical perception is a mechanism by which perceptual systems categorize continuously varying stimuli, making specific predictions about discrimination relative to category boundaries. Here we show that female zebra finches (Taeniopygia guttata) categorically perceive a continuously variable assessment signal: the orange to red spectrum of male beak colour. Both predictions of categorical perception5 were supported: females (1) categorized colour stimuli that varied along a continuum and (2) showed increased discrimination between colours from opposite sides of a category boundary compared to equally different colours from within a category. To our knowledge, this is the first demonstration of categorical perception of signal-based colouration in a bird, with implications for understanding avian colour perception and signal evolution in general.