Abstract Sex‐specific physiology is commonly reported in animals, often indicating lower immune indices and higher oxidative stress in males than in females. Sexual selection is argued to explain these differences, but empirical evidence is limited. Here, we explore sex differences in immunity, oxidative physiology and packed cell volume of wild, adult, breeding birds (97 species, 1997 individuals, 14 230 physiological measurements). We show that higher female immune indices are most common across birds (when bias is present), but oxidative physiology shows no general sex‐bias and packed cell volume is generally male‐biased. In contrast with predictions based on sexual selection, male‐biased sexual size dimorphism is associated with male‐biased immune measures. Sexual dichromatism, mating system and parental roles had no effect on sex‐specificity in physiology. Importantly, female‐biased immunity remained after accounting for sexual selection indices. We conclude that cross‐species differences in physiological sex‐bias are largely unrelated to sexual selection and alternative explanations should be explored.