The absence of a global-scale dynamo-generated magnetic field and the existence of an ionosphere at Venus and Mars caused many to predict that their solar wind interaction would be similar. After Pioneer Venus Orbiter (PVO) observations, it was concluded that the global aspects of the Venusian interaction could be well described by single-fluid models. According to these models, the magnetic field draping should develop progressively from the shock down to the ionopause. A recent study at Mars, where a Venus-like interaction was expected, showed that draping is prominent only inside the magnetic pileup boundary (MPB), a well-defined plasma boundary located between the shock and the ionopause first reported at comets, but never at Venus. From an identical analysis on PVO magnetometer data, we report a dramatic enhancement of draping on the dayside of Venus. Then, we deduce the existence of a Venusian counterpart of the Martian and cometary MPB.