Yes, this is a well-known phenomenon called the nocebo effect. For example, in one study patients were given a drug to treat prostate enlargement (finasteride). The researchers informed one group of the potential side effect of erectile dysfunction, but not the other group. 44% of the men who were informed of the side effect experienced it, while only 15% of the group who were not informed experienced it. So the opposite of the placebo effect does seem to occur as well.

http://www.nytimes.com/2012/08/12/opinion/sunday/beware-the-nocebo-effect.html?_r=0