Determining the pathogenicity of genetic variants is a critical challenge, and functional assessment is often the only option. Experimentally characterizing millions of possible missense variants in thousands of clinically important genes requires generalizable, scalable assays. We describe variant abundance by massively parallel sequencing (VAMP-seq), which measures the effects of thousands of missense variants of a protein on intracellular abundance simultaneously. We apply VAMP-seq to quantify the abundance of 7,801 single-amino-acid variants of PTEN and TPMT, proteins in which functional variants are clinically actionable. We identify 1,138 PTEN and 777 TPMT variants that result in low protein abundance, and may be pathogenic or alter drug metabolism, respectively. We observe selection for low-abundance PTEN variants in cancer, and show that p.Pro38Ser, which accounts for ~10% of PTEN missense variants in melanoma, functions via a dominant-negative mechanism. Finally, we demonstrate that VAMP-seq is applicable to other genes, highlighting its generalizability.