In meditation, you are removing distractions that you may have been using to distract yourself from how exhausted you may be. It could be that meditation is simply allowing you to clearly feel how much you really need a nap!
It could be something else too, of course, that's making you feel drowsy in meditation. Like maybe that's your body's response to feeling understimulated or overstimulated. You could try a different form of meditation, like a walking meditation or something else to meet those needs better. Either way, listen to your body and find out what it's telling you there in the quiet focus of meditation. Find what works for you!