The short answer is no, the word master does not denote masculinity.
The verb and adjective forms are utterly without controversy, and you could easily, intuitively write sentences like "She mastered the school's technique" or "She is a master bassist."
The noun form is only controversial to the most hardline traditionalists. Notwithstanding their objections from the fringes of society, you could otherwise write sentences like "She is master of the ship" without attracting argument.
Nor does the word master itself have a male-specific etymological base. It derives from the Latin magnus, which is a masculine word in the sense that Latin had a grammatical gender, but not in the sense that somehow the concept of magn- could only be applied to males. (And there was the feminine equivalent magna.)
So, whence does the controversy arise?
It's because, in the past, people believed that it was very important to know whether the holder of any given role was male or female. And they structured their societies--and gave so few rights to females--such that in many instances it actually was important to know. I'll get back to this point in a moment.
In modern times we have largely divorced roles from any explicit sex-specificity, and a person's sex therefore doesn't matter in the consideration of the roles that person performs. The chairperson's sex has no bearing on that person's ability to be chair, nor does the firefighter's sex, nor the waiter's, nor the actor's, and so forth.
But old ideas do not die easily, and there are still many people who insist that we should use role descriptors to also indicate a person's sex, even though the usefulness is obsolete. And there are bits and pieces in the English language onto which these diehard traditionalists cling.
The best such example, in the context of your query about the worst master, is the word mistress, the feminized corruption of master by way of Old French. In olden times many roles existed as sex pairs. A landed estate would have had a master, denoting that individual's authority over the affairs of his house. Quite often the master would have been married, and his wife would have been granted considerable parallel authority under her husband to govern those affairs of the house traditionally identified as being within the distaff domain (i.e., women's affairs). To convey this concept quickly, the word mistress arose to denote the master's female counterpart.
These days such a usage is virtually obsolete. Exceptions do still exist; the White House still has a traditional mistress-type role for the First Lady; nonetheless the role has become an anachronism as today most couples divide their domestic affairs circumstantially, without respect to sex, and with each successive generation this de-gendering of roles is becoming more thorough.
Be that as it may, the fact that the actual, historical role of mistress is obsolete poses no dissuasion to those who still believe that we must use roles to identify people's sex. To these traditionalists, a female of any sort of authority is a mistress, never a master, and thus, to them, the term master is masculine and reserved for male use (although they would not object to the verb and adjectival forms of the word).
I would be negligent to finish this reply without a few words on the feminine diminutive more broadly, of which mistress is but one instance. The most common feminine diminutives in English are -ess (as with mistress) and -ette (as with bachelorette). By their nature, feminine diminutives are degrading, implying that somehow for a female to hold a role means they alter the role itself to reflect their sex. The English-speaking world has been moving away from the feminine diminuative for a long time, and another commenter made an excellent example of this gradation in action by invoking the words waitress, which many people still accept (though some think of it as quaint), authoress, which virtually no one uses, and Jewess, which is nowadays used only as an offensive slur.
In all likelihood this trend will continue as society continues toward its recognition that a person's sex is independent of their capacity to fulfill a role, like that of author, and moreover that being a female does not make for an inferior individual. Specialized exceptions will linger the longest, like actress, because the film industry segregates awards.
Thus, for all the protestations of the hardliners, in my assessment you can safely ignore them and use master of females howsoever you wish.
Lastly, here's a bit of data: The words master and mistress have both in sustained long-term decline, with a minor resurgence recently that may or may not be statistical noise. Either way, the data suggest that the very concept of mastership is fading from the social currency, and with it the tagalong concept of the mistress. That's in addition to the decline in mistress as a result of our society becoming less sexist.