Winston Groom, author of Forrest Gump, answers this question by confirming that Jenny died of Hepatitis C. She contracted it during her era of sexual exploits while traveling with hippies and indulging in drugs and sex.
Hepatitis C is contracted through drug abuse and since the movie is set in the 1980s, the disease was unknown. The Hepatitis C virus came to light in 1989. This is why Jennie tells Forrest in the movie that she is dying from an unknown disease, due to the times.
Jenny was the love interest to the main character Forrest Gump, her death was shrouded in mystery towards the end of the movie. Considering she had married Forrest and they had a son together. Her death made fans of the movie assume that she died of HIV/AIDS, which at the time, had plausible reason seeing as she was sharing needles and having random sex which would lead to her contracting the disease.
However, she did marry Forrest and they did have a child together which would make both Forrest and the baby HIV positive. However that wasn’t the case, the movie shows that they did not contract the disease.