Membrane surface reconstruction at the nanometer scale is required for understanding mechanisms of subcellular shape change. This historically has been the domain of electron microscopy, but extraction of surfaces from specific labels is a difficult task in this imaging modality. Existing methods for extracting surfaces from fluorescence microscopy have poor resolution or require high-quality super-resolution data that is manually cleaned and curated. Here we present NanoWrap, a new method for extracting surfaces from generalized single-molecule localization microscopy (SMLM) data. This makes it possible to study the shape of specifically-labelled membraneous structures inside of cells. We validate NanoWrap using simulations and demonstrate its reconstruction capabilities on SMLM data of the endoplasmic reticulum and mitochondria. NanoWrap is implemented in the open-source Python Microscopy Environment.