Cylindrospermopsis (Raphidiopsis) raciborskii is an invasive, filamentous, nitrogen‐fixing cyanobacterium that forms frequent blooms in freshwater habitats. While viruses play key roles in regulating the abundance, production and diversity of their hosts in aquatic ecosystems, the role(s) of viruses in the ecology of C. raciborskii is almost unexplored. Progress in this field has been hindered by the absence of a characterized virus–host system in C. raciborskii. To bridge this gap, we sequenced the genome of CrV‐01T, a previously isolated cyanosiphovirus, and its host, C. raciborskii strain Cr2010. Analyses suggest that CrV‐01T represents a distinct clade of siphoviruses infecting, and perhaps lysogenizing, filamentous cyanobacteria. Its genome contains unique features that include an intact CRISPR array and a 12 kb inverted duplication. Evidence suggests CrV‐01T recently gained the ability to infect Cr2010 and recently lost the ability to form lysogens. The cyanobacterial host contains a CRISPR‐Cas system with CRISPR spacers matching protospacers within the inverted duplication of the CrV‐01T genome. Examination of metagenomes demonstrates that viruses with high genetic identity to CrV‐01T, but lacking the inverted duplication, are present in C. raciborskii blooms in Australia. The unique genomic features of the CrV/Cr2010 system offers opportunities to investigate in more detail virus–host interactions in an ecologically important bloom‐forming cyanobacterium.