Yes, it is permissible for her servant to shave her pubic hair for her, because there is a need for that. This was stated by the fuqaha’ (may Allaah have mercy on them).
Al-Mardaawi (may Allaah have mercy on him) said in al-Insaaf (8/22):
If a person is serving a sick man or woman by helping them to do wudoo’ or istinja’ (washing the private part after relieving oneself) etc, the ruling is the same as that on a doctor with regard to looking and touching. This was stated by Imam Ahmad (may Allaah have mercy on him). The same applies if (the servant) shaves the pubic hair for one who is unable to do that. This was stated by Imam Ahmad and by Abu’l-Wafa’ and Abu Ya’la the younger. End quote.
And it says in Kashshaaf al-Qinaa’ (5/13):
A doctor may look at and touch whatever he needs to look at and touch, even a woman’s private part and the inside of it, because this is a case of necessity… But that should be in the presence of a mahram or husband, because when two people are alone together (khulwah) there is always the risk of something wrong happening. And anything other than the part that needs to be examined should be covered, because the basic principle that it is forbidden remains in effect.
The same applies to the one who is serving a sick man or woman by helping them to do wudoo’ or istinja’ (washing the private part after relieving oneself) etc, or who is saving someone who is drowning or trapped in a burning building and so on, or by shaving the pubic hairs of one who is not able to do that. End quote.
For a male doctor to treat a female patient is subject to certain conditions, e.g. if there is no female doctor available, even if she is a non-Muslim.
See the answer to question no. 5693.