We report the complete 2,783,931-bp circular genome sequence of the human methicillin-resistant strain Staphylococcus aureus 17Gst354, isolated from a nasal swab. The strain possessed an additional 4,397-bp plasmid. Moreover, we induced and sequenced its temperate phage Staphylococcus phage vB_StaphS-IVBph354, which has a circular genome of 41,970 bp.