We present a new method, CIDER-Seq (Circular DNA Enrichment sequencing) for the unbiased enrichment and long-read sequencing of viral-sized circular DNA molecules. We used CIDER-Seq to produce single-read full-length virus genomes for the first time. CIDER-Seq combines PCR-free virus enrichment with Single Molecule Real Time sequencing and a new sequence de-concatenation algorithm. We apply our technique to produce >1200 full-length, highly accurate geminivirus genomes from RNAi-transgenic and control plants in a field trial in Kenya. Using CIDER-Seq we can demonstrate for the first time that the expression of antiviral double-stranded RNA (dsRNA) in transgenic plants causes a consistent shift in virus populations towards species sharing low homology to the transgene derived dsRNA. Our method and its application in an economically important crop plant opens new possibilities in periodic virus sequence surveillance and accurate profiling of diverse circular DNA elements.