Deletion of functional sequence is predicted to represent a fundamental mechanism of molecular evolution1,2. Comparative genetic studies of primates2,3 have identified thousands of human-specific deletions (hDels), and the cis-regulatory potential of short (≤31 base pairs) hDels has been assessed using reporter assays4. However, how structural variant-sized (≥50 base pairs) hDels influence molecular and cellular processes in their native genomic contexts remains unexplored. Here, we design genome-scale libraries of single-guide RNAs targeting 7.2 megabases of sequence in 6,358 hDels and present a systematic CRISPR interference (CRISPRi) screening approach to identify hDels that modify cellular proliferation in chimpanzee pluripotent stem cells. By intersecting hDels with chromatin state features and performing single-cell CRISPRi (Perturb-seq) to identify their cis- and trans-regulatory target genes, we discovered 19 hDels controlling gene expression. We highlight two hDels, hDel_2247 and hDel_585, with tissue-specific activity in the liver and brain, respectively. Our findings reveal a molecular and cellular role for sequences lost in the human lineage and establish a framework for functionally interrogating human-specific genetic variants.