Before saying "yes", I'd be concerned whether or not the cabinet can carry the weight (including the weight of the stuff you put in the cabinet.) My best guess is "yes" - microwaves really aren't that heavy, compared to what could be put into cabinets. But, I don't know what the quality of your cabinets is, whether they might sag over time, etc. What's directly above the cabinet? Can you reinforce it all the way up into the ceiling or soffit or whatever's above the cabinets?
edit: OP, search for information related to mounting microwaves under cabinets that are in a kitchen island. They make special mounting kits (if your microwave doesn't have one). I realized that this sounds like what you might be trying to do. Another thing to factor in - is your cabinet mounted correctly? That is, are all of the screws/bolts firmly anchored into structural members?
edit edit: if mounting to the bottom of your cabinet, those screws/bolts better penetrate into the cabinet and have large washers to distribute the weight. Else, you're going to have some holes in the bottom of the cabinet where they pulled through (which will be the least of your concerns at that point.) Googling for some weights - I'm seeing 50-60 pounds. I'm pretty sure I have that much weight in the cabinet with my dishes in it; I just don't know how much more weight that cabinet can take. Thus, the weight, okay - but once you include the weight of what else is in the cabinet, and weight of the food in the microwave (I can't think of any time I have more than 6 or 7 pounds in the microwave)...