As a prelude to the answer, it should be understood that it is obligatory (Wājib) to allow the beard to grow. Furthermore, it is unlawful, and a grave sin to shave or cut the beard less than a fist length. However, despite the aforementioned ruling, there is a conditional leeway (when and as much as necessary) in the light of Shari’ah rules and precedents for shaving the beard, if required to do so, in exceptional circumstances. The precedents and conditions are outlined below:
1. It is obligatory for a person to protect his life, and it is unlawful and haram to intentionally kill oneself or to put oneself in clear danger except for the exceptional scenarios mentioned in Shariah (‘Azeemah).
2. The verse of the Holy Quran proves that in order to save one's life, it is permissible to perform a forbidden act in a situation of extreme compulsion (when and as much as necessary), just as the Islamic jurists have given conditional permission to eat food (such as pig and wine) which is considered haram (forbidden) in times of starvation and fear of death.
3. Hanafi jurists have forbidden women to cut their hair, but it is permissible conditionally to shave one's head if there is a legal need in the Shari’ah.
4. Similarly, in the Maliki School of fiqh, it is explicitly stated that shaving one's beard under normal circumstances is considered defacing and a religious innovation (bid’ah), but if there is a wound that requires one to cut or shave the beard for proper treatment, it is permissible to do so.
5. Keeping a beard is an act of worship and the right of Allah ﷻ on an individual. Whereas saving lives of others and to refrain from causing harm to them, is the right of people on an individual. The right of people appears to take precedence (in the mentioned situation) over the right of Allah ﷻ.
Considering the above statements, If in the scenario mentioned in the question, where it has been declared as mandatory for physicians to use the N-95 mask in order to protect their life from the COVID-19 disease, and if according to Muslim medical experts, the mask will protect a physician only if the mask is well adhered to the skin of the face, furthermore, the physicians consider it necessary to shave the beard in order to protect their lives by using N-95 mask, alongside that, if there is reasonable surety or preponderance of opinion by overpowering thought (ghalib al-zann) that wearing the mask will safeguard the lives of the physician, patient and others, then there is leeway found as long as the following conditions are met;
1. This will only be allowed to the physicians who are exposed to the COVID-19 patients directly (f2f), or have been given the responsibility of diagnosing and treating the disease and they were not able to clear the fit-test because of their beard.
2. If there is no other alternative available to the physician (like PAPR), which allows them to keep their beard, or the alternative is not within the reach or accessible to the physician.
3. Only that part of the beard should be trimmed or shaved that would help meet the requirement to wear a specific mask (N-95).
If the above conditions are not met, it is not permissible to cut the beard shorter than the required obligatory length.
Note: The doctor who shaves or cuts the beard should make a firm intention that as soon as the need caused by the epidemic disappears, he would regrow his beard to the required length. In addition, it is appropriate for such a person to continue to repent and seek forgiveness at the same time.