The aim of this study was to evaluate the performance, milk composition, blood and urinary biochemical parameters and milk fatty acid profile of Saanen goats fed pornunça silage‐based diets containing different levels of tannin (11, 28, 36 and 44 g/kg dry matter). Intake of feed, milk production, milk composition and biochemical parameters were affected (P < 0.05). The content of 10:0, 12:0 and 14:0 fatty acids decreased, while those of 18:0, cis‐9 18:1, trans‐11 18:1, cis‐9, trans‐11 18:2 and cis‐9, cis‐12, cis‐15 18:3 increased as more tannin was added (P < 0.05). The ratio of unsaturated to saturated fatty acids increased, while the thrombogenicity and atherogenicity indices decreased as tannin was increased (P < 0.05). The inclusion of up to 28 g/kg of tannin was the most appropriate level to improve the fatty acid profiles of goats’ milk and prevent further falls in dry matter intake and milk production.