Like a halloween mask to conceal injuries of a burn?
Of course. If there's a medical reason for it and the student can produce an appropriate doctor's certificate or what not. You would need to check the regulations.
It probably depends on what sort of mask it is. If the mask is distracting for other students or plain silly, then I can imagine that it is reasonable to object to it. So, 'halloween mask' may not be the best description of an appropriate mask.