It is not permissible for a female doctor to take off her hijab when visiting patients, even if the laws governing her work require her to do that

Praise be to Allah.

Specialising in medicine, for practising sisters, is a good thing if it is free of fitnah and temptation in school and at work, and it does not involve anything that is contrary to Islamic teachings. 

With regard to things that are required for the purpose of learning and practising the profession, such as seeing or touching ‘awrahs, that is permissible as it is a case of need, as we have explained in the answer to question no. 169979 

Wearing hijab in front of non-mahram men is a definite obligation as is indicated by the Qur’an, Sunnah, and scholarly consensus. Hence it is not permissible for anyone to instruct a woman to do the contrary or to prevent a woman who wants to comply with that. By the same token, it is not permissible for a woman to take this obligation lightly or to uncover any part of her body, unless she is compelled to do that by a case of necessity which makes that which is ordinarily prohibited permissible. 

With regard to going out to work, if she does not need to do that, because the maintenance of her husband or father or whoever is obliged to spend on her, be he a relative or otherwise, is sufficient, then it is not permissible for her to go out to work if that will result in her taking off the hijab. 

Please see the answer to question no. 93145. 

Based on the above: 

If you do not need to work, rather you want to work in the medical field because there is a great need for women specialists in this area, and this work of yours will result in mixing with non-mahram – and kaafir – men, and coming under non-Islamic law that does not pay attention to the rulings of Islamic sharee‘ah, and this will result in you having to do things that are contrary to what is enjoined by Allah and His Messenger, i.e., not covering and observing hijab, and will also lead to temptation and exposing oneself to the wrath and punishment of Allah, then what we advise you to do is not to take on this profession, and to look for other kinds of work in which you will be able to benefit the Muslims. 

But if it is possible for people of wealth and means among the Muslim community in that country to cooperate in establishing a specialist hospital, paying attention to the rulings of Islam and the situation of poor and needy Muslim is, in which all medical specialties are available, then this would be a blessed project. In this case you could work there and preserve your modesty and hijab, and not have to go against any of the commands of Allah, may He be exalted, and His Messenger (blessings and peace of Allah be upon him). 

And Allah knows best.