A genetic virus was a type of virus relating to DNA.
A deadly genetic virus was used by The Albino to kill Kang's son, Dax, as well as the sons of Kor and Koloth. This lead these Klingons and Curzon Dax, the namesake of Kang's son, to swear a blood oath to cut out the Albino's heart. (DS9: "Blood Oath")
In the novel Forged in Fire, the disease – which was actually a retrovirus given to the Klingons to pass to their sons – was a modification of the bacteriological virus of Omega IV. The novel states that The Albino also infected Sulu with the virus, but due to his immunity built up during "The Omega Glory", he was unaffected by it.
In 2374, The Doctor discovered a second DNA pattern in Tom Paris's nucleotide structure and reasoned that it might be a genetic virus. (VOY: "Vis à Vis")