The residence of dinoflagellate algae (genus: Symbiodinium) within scleractinian corals is critical to the construction and persistence of tropical reefs. In recent decades, however, acute and chronic environmental stressors have frequently destabilized this symbiosis, ultimately leading to coral mortality and reef decline. Viral infection has been suggested as a trigger of coral–Symbiodinium dissociation; knowledge of the diversity and hosts of coral-associated viruses is critical to evaluating this hypothesis. Here, we present the first genomic evidence of viruses associated with Symbiodinium, based on the presence of transcribed +ss (single-stranded) RNA and ds (double-stranded) DNA virus-like genes in complementary DNA viromes of the coral Montastraea cavernosa and expressed sequence tag (EST) libraries generated from Symbiodinium cultures. The M. cavernosa viromes contained divergent viral sequences similar to the major capsid protein of the dinoflagellate-infecting +ssRNA Heterocapsa circularisquama virus, suggesting a highly novel dinornavirus could infect Symbiodinium. Further, similarities to dsDNA viruses dominated (∼69%) eukaryotic viral similarities in the M. cavernosa viromes. Transcripts highly similar to eukaryotic algae-infecting phycodnaviruses were identified in the viromes, and homologs to these sequences were found in two independently generated Symbiodinium EST libraries. Phylogenetic reconstructions substantiate that these transcripts are undescribed and distinct members of the nucleocytoplasmic large DNA virus (NCLDVs) group. Based on a preponderance of evidence, we infer that the novel NCLDVs and RNA virus described here are associated with the algal endosymbionts of corals. If such viruses disrupt Symbiodinium, they are likely to impact the flexibility and/or stability of coral–algal symbioses, and thus long-term reef health and resilience.