Determining the pathogenicity of human 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 will likely require generalizable, scalable assays. Here 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 in a single experiment. We apply VAMP-seq to quantify the abundance of 7,595 single amino acid variants of two proteins, PTEN and TPMT, in which functional variants are clinically actionable. We identify 1,079 PTEN and 805 TPMT single amino acid 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 our abundance data suggest that a PTEN variant accounting for ~10% of PTEN missense variants in melanomas functions via a dominant negative mechanism. Finally, we demonstrate that VAMP-seq can be applied to other genes, highlighting its potential as a generalizable assay for characterizing missense variants.