Incoming simian virus 40 (SV40) particles enter tight-fitting plasma membrane invaginations after binding to the carbohydrate moiety of GM1 gangliosides in the host cell plasma membrane through pentameric VP1 capsid proteins. This is followed by activation of cellular signalling pathways, endocytic internalization and transport of the virus via the endoplasmic reticulum to the nucleus. Here we show that the association of SV40 (as well as isolated pentameric VP1) with GM1 is itself sufficient to induce dramatic membrane curvature that leads to the formation of deep invaginations and tubules not only in the plasma membrane of cells, but also in giant unilamellar vesicles (GUVs). Unlike native GM1 molecules with long acyl chains, GM1 molecular species with short hydrocarbon chains failed to support such invagination, and endocytosis and infection did not occur. To conceptualize the experimental data, a physical model was derived based on energetic considerations. Taken together, our analysis indicates that SV40, other polyoma viruses and some bacterial toxins (Shiga and cholera) use glycosphingolipids and a common pentameric protein scaffold to induce plasma membrane curvature, thus directly promoting their endocytic uptake into cells.