How about simply the word masculine?
This wasn't random, as I believe it clearly relates to the question: if distaff is taken to mean "the female equivalent of something typically male", then the desired antonym should mean "the male equivalent of something typically female", no? Honestly, 'male' is the word I would have suggested, but that's already been suggested and rejected, so I chose a related word which had yet to be suggested.
Judging by MετάEd's comment, it needs to also (or perhaps instead) express 'paternal', which changes the desired definition to be something like "the paternal equivalent of something typically female". To me, however, 'paternal' doesn't necessarily imply 'male', as it brings to table the issue of gender roles, which is, I believe, outside the scope of the question.
Distaff, being used as a modifier in phrases such as "marriage is still the passport to distaff power", would be taken to mean "of or concerning women"1. Having learned this, and using 'masculine' to mean "having qualities traditionally associated with men; manly; virile," I can see that the word doesn't quite encompass what we need for either this definition or the OP's: masculine encompasses a set of characteristics typically attributed to men, and is, to a great extend, subjective; it is not a word that is directly tied to something that is male or a male equivalent.
Having now considered the matter further, I would suggest something which builds on the root andro-, the Greek root for 'man' or 'male'. Also, perhaps, the word should end with -al, from the Latin suffix meaning 'of or pertaining to'.