Nine complete nucleotide sequences of geminialphasatellites (subfamily Geminialphasatellitinae, family Alphasatellitidae) recovered from the wild Poaceae Sorghum arundinaceum collected in Reunion are described and analyzed. While the helper geminivirus was identified as an isolate of maize streak virus (genus Mastrevirus, family Geminiviridae), the geminialphasatellite genomes were most closely related to, and shared ~63% identity with, clecrusatellites. Even though the geminialphasatellite molecules lack an adenine rich-region, they have the typical size of geminialphasatellites, encode a replication-associated protein in the virion sense, and have probable stem-loop structures at their virion-strand origins of replication. According to the proposed geminialphasatellite species and genus demarcation thresholds (88% and 70% nucleotide identity, respectively), the genomes identified here represent a new species (within a new genus) for which we propose the name “Sorghum mastrevirus-associated alphasatellite” (genus “Sorgasalphasatellite”).