The ‘shock and kill’ approach to cure human immunodeficiency virus (HIV) includes transcriptional induction of latent HIV-1 proviruses using latency-reversing agents (LRAs) with targeted immunotherapy to purge infected cells. The administration of LRAs (panobinostat or vorinostat) to HIV-1-infected individuals on antiretroviral therapy induces a significant increase in cell-associated unspliced (CA-US) HIV-1 RNA from CD4+ T cells. However, it is important to discern whether the increases in CA-US HIV-1 RNA are due to limited or broad activation of HIV-1 proviruses. Here we use single-genome sequencing to find that the RNA transcripts observed following LRA administration are genetically diverse, indicating activation of transcription from an extensive range of proviruses. Defective sequences are more frequently found in CA HIV-1 RNA than in HIV-1 DNA, which has implications for developing an accurate measure of HIV-1 reservoir size. Our findings provide insights into the effects of panobinostat and vorinostat as LRAs for latent HIV-1.