A microscopic formalism to treat α decay from superdeformed nuclei is given within the framework of the Hartree-Fock-Bogoliubov approximation. The process of penetration through the deformed barrier is described exactly. The influence of the deformation on the formation amplitude and on the penetrability is analyzed. It is found that the results of the WKB approximation differ strongly from the exact ones as the deformation increases for β2 larger than 0.3. The most favorable case that we found corresponds to a superdeformed band in 192Pb, for which the α decay probability is very large, making this a likely mechanism to feed the daughter nucleus 188Hg.