Cellular function depends on dynamic interactions and nanoscale spatial organisation of proteins. While transcriptomic and proteomic methods have enabled single-cell profiling, scalable technologies allowing high-resolution analysis of protein interactions at omics-scale are lacking. Here we present the Proximity Network Assay (PNA), a DNA-based method for constructing three-dimensional nanoscale maps of 155 proteins in single cells without the use of optics. PNA employs barcoded antibodies and in situ rolling circle amplification to generate >40,000 spatial nodes per cell, which are linked through proximity-dependent gap-fill ligation and decoded by DNA sequencing, forming single cell Proximity Networks. At an estimated spatial resolution of [~]50 nm, PNA captures single-cell protein abundance, self-clustering, and colocalization, validating established cell membrane protein interactions. We illustrate how PNA can be used to gain insights into the molecular mechanisms of cell function through protein interactions in hematological oncology, CAR-T cell therapies, and autoimmune disease.