Here's what Dr. Thomas Hale says in the must-have guide to medications and breastfeeding, Medications and Mothers' Milk:
Beer, but not ethanol, has been reported in a number of studies to stimulate prolactin levels and breastmilk production. Thus is it presumed that the polysaccharide from barley may be the prolactin-stimulating component of beer. Non-alcoholic beer is equally effective.
Dr. Hale also cites two studies which suggest that, in the immediate period after mothers consume alcohol, milk production declines significantly and babies take in less milk.
So it appears that barley, a traditional food for increasing milk supply, makes beer effective at increasing prolactin levels, but that the alcohol in it causes babies to take in less milk.
Of course, drinking alcohol while breastfeeding can pose risks for your baby if it's not consumed in moderation. And beer, non-alcoholic or not, would not be the at the top of the list of recommendations for increasing milk supply.