Prenatal detection of congenital heart disease facilitates the opportunity for potentially life-saving care immediately after the baby is born. Echocardiography is routinely used for screening of morphological malformations, but functional measurements of blood flow are scarcely used in fetal echocardiography due to technical assumptions and issues of reliability. Magnetic resonance imaging (MRI) is readily used for quantification of abnormal blood flow in adult hearts, however, existing in utero approaches are compromised by spontaneous fetal motion. Here, we present and validate a novel method of MRI velocity-encoding combined with a motion-robust reconstruction framework for four-dimensional visualization and quantification of blood flow in the human fetal heart and major vessels. We demonstrate simultaneous 4D visualization of the anatomy and circulation, which we use to quantify flow rates through various major vessels. The framework introduced here could enable new clinical opportunities for assessment of the fetal cardiovascular system in both health and disease.