Time irreversibility, a fundamental property of nonequilibrium systems, should be of importance in assessing the status of physiological processes that operate over a wide range of scales. However, measurement of this property in living systems has been limited. We provide a computational method derived from basic physics assumptions to quantify time asymmetry over multiple scales and apply it to the human heartbeat time series in health and disease. We find that the multiscale time asymmetry index is highest for a time series from young subjects and decreases with aging or heart disease. Loss of time irreversibility may provide a new way of assessing the functionality of living systems that operate far from equilibrium.