A protein at equilibrium is commonly thought of as a fully relaxed structure, with the intra-molecular interactions showing fluctuations around their energy minimum. In contrast, here we find direct evidence for a protein as a molecular tensegrity structure, comprising a balance of tensed and compressed interactions, a concept that has been put forward for macroscopic structures. We quantified the distribution of inter-residue prestress in ubiquitin and immunoglobulin from all-atom molecular dynamics simulations. The network of highly fluctuating yet significant inter-residue forces in proteins is a consequence of the intrinsic frustration of a protein when sampling its rugged energy landscape. In beta sheets, this balance of forces is found to compress the intra-strand hydrogen bonds. We estimate that the observed magnitude of this pre-compression is enough to induce significant changes in the hydrogen bond lifetimes; thus, prestress, which can be as high as a few 100 pN, can be considered a key factor in determining the unfolding kinetics and pathway of proteins under force. Strong pre-tension in certain salt bridges on the other hand is connected to the thermodynamic stability of ubiquitin. Effective force profiles between some side-chains reveal the signature of multiple, distinct conformational states, and such static disorder could be one factor explaining the growing body of experiments revealing non-exponential unfolding kinetics of proteins. The design of prestress distributions in engineering proteins promises to be a new tool for tailoring the mechanical properties of made-to-order nanomaterials.