As far as I understand, this matter is entirely separate from any other fallout — read: legal action — that may yet occur from the incident between Jose Mourinho and the Chelsea medical team at the tail end of the 2-2 draw against Swansea City. I have not found any official statement from The FA about this investigation, but Sam Wallace of The Independent claims that one has been made, so let's go with that.
In a statement the FA said: "The FA has received an enquiry relating to an alleged incident during the Premier League fixture between Swansea v Chelsea on 8 August, and will make no further comment at this time."
According to Wallace, the complaint, made by a member of the public and which The FA are "duty-bound" to investigate, refers to the incident of Mourinho using abusive language towards Dr. Carneiro. The complaint appears to not mention physio Jon Fearn, which raises the added possibility of this being classified an "aggravated breach" of FA rule E3 (i.e. sexist language). If found guilty of improper conduct, the minimum punishment is a five-match ban.
GENERAL BEHAVIOUR — E3
(1) A Participant shall at all times act in the best interests of the game and shall not act in any manner which is improper or brings the game into disrepute or use any one, or a combination of, violent conduct, serious foul play, threatening, abusive, indecent or insulting words or behaviour.
(2) A breach of Rule E3(1) is an "Aggravated Breach" where it includes a reference, whether express or implied, to any one or more of the following :- ethnic origin, colour, race, nationality, religion or belief, gender, gender reassignment, sexual orientation or disability.
(i) Where a Participant commits an Aggravated Breach of Rule E3(1) for the first time, a Regulatory Commission shall impose an immediate suspension of at least five matches on that Participant. The Regulatory Commission may increase this suspension depending on any additional aggravating factors present.
If you've been living under a rock and wondering what all this entirely avoidable, unnecessary, reprehensible incident is all about, here it is again.
Afterwards, Mourinho called the medical team "naive" and removed them both (temporarily, was the official word) from matchday duties. All of this of course could've been done privately, just as the club always insists on handling personnel issues, but Mourinho (and Carneiro, too, with her Facebook post) made it public. This whole fiasco has been just one of the many things to cast a pall over the club during this early season malaise.
What's done is done and now we face the fallout. According to reports, Carneiro has not returned to her duties at the club (which still involve being the first-team doctor). I've not seen what Jon Fearn may be up to, but nobody really cares about him anyway. (Sorry, Jon!)
It should be noted that neither Wallace's report nor The FA's investigation into this complaint guarantee a ban or any disciplinary action. As far as the futures of both Carneiro and Fearn, that's even murkier.