That depends on how you look at it.
If you take the approach of isolating diseases, and delivering specific disease causing agents to a target, its a strictly 20th Century development. The first attempts at it were made in World War I, then banned by the Geneva Accords. Terrorists and rogue nations continue to seek out such weapons, and use them on small scales (e.g. anthrax letters).
If you take the approach of just causing disease in a population, it goes back much farther. In Medieval days, siege forces would use their catapults to hurl dead animals and their camp's human waste over the walls, hoping to contaminate food and water supplies, and cause disease inside the castle, killing off the defenders.