At the time that Alfred Nobel wrote his will in 1895, biology was a very young science and its major contributions to society were through physiology and medicine. I'm sure he felt that these two areas covered all the useful advancements in the life sciences at the time (I mean would you want to be less specific and have your money go to the eugenics movement that was popular in biology at the time?). The subject of modern genetics & molecular biology didn't really start until the early 1900s with the rediscovery of Mendel, and that was after the Nobel Prize was established.
In fact, the problem of "what area to give molecular biologists a Nobel Prize in" has been there from the beginning as the Nobel Prize in 1907 was given to Eduard Buchner for isolating the first enzymes from a yeast extraction. They really couldn't give him a Nobel Prize in medicine or physiology for that, so they ended up just giving him the Nobel Prize in chemistry. Much to the dismay of inorganic chemists, this trend of giving out molecular biology awards under the Nobel Prize for "chemistry" continues to this day...in fact, every year I see chemists complaining about how the biologists are always getting the nobel prize for chemistry.