Tensegrity, or tensional integrity, is a property of a structure indicating a reliance on a balance between components that are either in pure compression or pure tension for stability. Tensegrity structures exhibit extremely high strength-to-weight ratios and great resilience, and are therefore widely used in engineering, robotics and architecture. Here, we report nanoscale, prestressed, three-dimensional tensegrity structures in which rigid bundles of DNA double helices resist compressive forces exerted by segments of single-stranded DNA that act as tension-bearing cables. Our DNA tensegrity structures can self-assemble against forces up to 14 pN, which is twice the stall force of powerful molecular motors such as kinesin or myosin. The forces generated by this molecular prestressing mechanism can be used to bend the DNA bundles or to actuate the entire structure through enzymatic cleavage at specific sites. In addition to being building blocks for nanostructures, tensile structural elements made of single-stranded DNA could be used to study molecular forces, cellular mechanotransduction and other fundamental biological processes.