You can thank William Randolph Hearst, the duPont family and Andrew Mellon for this.
Hearst was a newspaper tycoon who owned millions of acres of timber forests and a number of paper mills, while duPont held the patent for turning wood pulp into paper. However the process for turning wood into paper is relatively expensive (not to mention polluting) compared to making paper from hemp. Hemp, while very closely related to marijuana, contains virtually no THC, the chemical in cannabis that makes you high.
If hemp paper were to become commonplace, Hearst's forests and duPont's paper patents would be worthless. Hearst used his newspapers to begin spreading lies about the effects of marijuana. He took advantage of the highly racist attitudes of the time and ran articles about the prevalence of marijuana use among Mexican immigrants. Hearst deliberately tried to blur the line between marijuana and hemp, so that people eventually began to see them as the same thing. Even today, if you ask someone what hemp is, they'll likely reply "marijuana".
Meanwhile, one of duPont's financial backers, Andrew Mellon, also happened to be Secretary of the Treasury. He named his nephew-in-law Harry Anslinger as head of the Bureau of Narcotics. Anslinger wrote the Marijuana Tax Act of 1937, which required all marijuana, cannabis and hemp growers to purchase a $1 tax stamp (that's about $15 in 2010 dollars). Of course, actually obtaining the stamps was all but impossible. The Marijuana Tax Act was declared unconstitutional in 1969 and for a short time, marijuana was legal again, until the passing of the Controlled Substances Act in 1970.
The American Medical Association objected to the Marijuana Tax Act. Even back in the 1930s the medical community knew about the medicinal effect of cannabis.