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.
You will definitely need to check regulations regarding the wearing of costumes that conceal one's appearance. For example, in France it's forbidden by law to conceal one's face in public space, including in universities (and it's made explicit in universities' by-laws). While there's normally allowances made for legitimate medical reasons, there will definitely be limits. "Halloween-style" costumes and masks will probably be disallowed.
One additional comment not mentioned in Dave's answer is that in cases of laboratories and other "practical" exercises, such costumes may be disallowed for legal and protective reasons. You will need to talk with the appropriate staff about any accommodations that can be made.
In general, I second Dave's answer. There is one point, however. During exams students have to identify themselves, and this is commonly done by showing some identification document (e.g., student id) to the person in charge. Wearing a mask would likely be interpreted as a failure to identify yourself, unless identification is possible in some other way. As a rule, failing to identify yourself at our university means that the lecturer is not allowed to grade the exam. However, if wearing a mask is required due to a medical condition, the student can notify the examination board before the exam that can decide to deviate from the identification rule and oblige the lecturer to grade the exam.