Status: Probably real
eKantipur.com (a Nepalese website) has reported the birth of a severely deformed child
to a woman in Dolakha. (Warning: the newspaper article contains a possibly disturbing image.) The poor child looks a bit like a mutant muppet doll and created quite a stir in Nepal:
The news about such a baby being brought to the hospital spread like wildfire and there were hundreds gathered at the hospital to have a look. The police had to be deployed to control the crowd.
Someone left a note on the Wikipedia page for April 1, 2006
speculating that the child had anencephaly
(a neural tube defect which results in the absence of a major portion of the brain, skull, and scalp). This strikes me as plausible... more plausible than the idea that the baby shown in the picture is an elaborately crafted hoax. (Thanks to Sara for the link... She notes that it looks like a character from The Oblongs TV show.)