There are many references to the fact that Poe became ill after a small amount of alcohol. A brief search found this one from the E. A. Poe Society of Baltimore that has perhaps the best site dedicated to Poe.
"We must be careful accepting every statement about Poe's drinking at face value. Poe's enemies, and others who should know better, often attributed any reference to Poe being ill as another occasion of drinking. Although it appears that more than one or two drinks made Poe very ill, it is unreasonable to assume that he was never ill from other, and more commonplace, causes."
http://www.lfchosting.com/eapoe/GENINFO/poealchl.htm
That comment isn't as strong as it should be, because Poe seldom darnk alcohol at all. He knew perfectly well that it would make him sick very quickly. Rumors that he drank heavily were created by his in-laws, who didn't like him much, and by others who disliked him. In the 1990's there were several books and/or articles about his drinking that brought out his intolerance for article. There also was a piece of historical forensics that stated that the symptoms described during the time when he was in a hospital strongly suggest that he died of hydrophobia. The only thing that suggested that he might have been drinking was that he was found unconscious in a road.
I will take a careful look at the Wikipedia article and suggest correction, if that is called for.