There are two parts here: 1)
Why human?
How do you know it's a human voice?
Out of universe, we know Majel Barrett is human, and we know that she also played Christine Chapel and Number One
(the unnamed second officer under Captain Pike), both humans.
But she also played Lwaxana Troi, a Betazoid.
And there's nothing in the voice (as far as I can tell) to distinguish it from that of a Bajoran or a Vulcan or any other species.
The voice doesn't seem to be Klingon or Ferengi, but that might just be because it's flat, emotionless, and, well, computer-like.
2)
Why female?
In-universe (although quasi-canonically), it was Number One who installed the first voice device on the Enterprise and programmed it with her own voice.
(This is from Memory-Beta , which cites the novels "The Rift" and "Enterprise: The First Adventure").
She's a human female, so there you go.
Somewhat speculatively, there is some evidence that both men and women find women's voices more pleasing.
Research suggests that this might be due to the early bonding between fetuses/infants and their mother.
I bet that in a galaxy where there are hundreds of starships using a single programmed voice to get information from the computer -- sometimes in the middle of crisis -- the exact pitch and timbre of the voice has been thoroughly researched.
scifi.stackexchange.com/users/1973/Plutor
From "The Making of Star Trek", written by Stephen E Whitfield, and Gene Roddenberry (first published 1968, ISBN 1-85286-363-3, in the "Part II, An Official Biography of a Ship and its Crew", Chapter 2, page 152 it says: It [the computer] uses a feminine voice, a familiar occurrence, even today.
The pre-take-off system on today's F-105 Fighter, for example, speak to the pilots in a female voice because it has been discovered that the feminine voice penetrates noise better and results in improved response by men (and women).
If that's enough for a TV show being made in the 60s, it'd probably be a good enough in-show reason :-)
While I'm not sure it's ever noted during an episode, in "Mirror, Mirror", in TOS, this was the reason why the Mirror Universe computers spoke with a male voice - because it was suggested that in the mirror universe they never did that piece of research, and as a result just used a default male voice instead.
(You also see Kirk & McCoy doing a double take when they hear the computer talking)
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There's never any in-universe reason given for the computer's voice being female but in the real world female voices are easier to understand and more pleasant to listen to according to this CNN article.
I believe this is also the reason most police dispatchers are female.
Though it's entirely possible that the use of female voices for computers was influenced by Star Trek itself.
scifi.stackexchange.com/users/1224/Brian Ortiz
Low-pitched audio frequencies ("bass") are harder to reproduce (cf. subwoofers - dedicated equipment for that)
than the high-pitches ones.
So, when it does not matter who the speaker is - e.g., when the sound is computer-generated - it is easier to use female voices.
This is why the vast majority of voices coming out of loudspeakers are female.
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It was the voice of Gene Roddenberry's wife, who also played Nurse Chapel on the original show.
Gene thought it would be cool to have a sexy computer voice, since at that point, voices of comupters were robotic and male.
He thought his wife's voice was very sexy, so he asked her.
It was also a way to show how futuristic Star Trek was, too
, i.e. - you could make the computer sound any way you wanted.
And Kirk, being a lady-killer would naturally choose a sexy-lady voice.
scifi.stackexchange.com/users/1165/bev
ships are called with women names.
and even though the enterprise is not a woman name they refer it as "she".
humanity might follow traditions and traits of the older kind and respect the old times so that would mean a woman voice in the ship is tradition and respect, as for real life story Gene Roddenberry loved hsi wife
so he deiced to make her the voice of the computer
scifi.stackexchange.com/users/16244/The Extinct Surgeon
One reason for a female voice: real world aircraft cockpit warning systems use recorded female voices because they're known to be more effective at getting flight crews' attention in complicated situations.
I'm not sure if this applies equally to female pilots, but I wouldn't be surprised if it did.
scifi.stackexchange.com/users/2764/Russell Borogove
Flight systems (fighter jets) have female voices because they (used to) stand out of the radio chatter (which used to be all male).
Nowadays there's some systems that use a male voice.
Given there's translation everywhere I'd imagine only humans hear a human voice, the rest something more suited to their species.
Why female?
Ask the guys who designed the communication system ;).
My other answer is: it was 50/50 and then it just became standard.
If you don't like it ask the computer to reconfigure for you personally.
scifi.stackexchange.com/users/5132/Lodewijk
Not specific to Star Trek, but general to most computers in movies or real life having a female voice: A voice system for most of them fills the role of a secretary.
You make the decisions, the secretary collects/handles/organizes/reports the information.
Most secretaries were and still are, female.
While probably not the sole cause, traditions can have an important effect on shaping our views and expectations.
scifi.stackexchange.com/users/4004/vsz
In Star Trek all Federation computers have a human female voice, provided by Gene Roddenbery's wife Majel Barrett.  This, of course, is the out of universe reason; however is there ever an in universe reason given?  With the Federation being a multi-gender, multi-species organization why a humanoid female voice?  Is the voice based on someone related to the LCARS systems?
Why does the computer have a human female voice?
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<star-trek><star-trek-tng><star-trek-voyager><star-trek-ds9>
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scifi.stackexchange.com/users/8226/Monty129
Gene Roddenberry thought it would be a good idea to have a sexy computer voice, since up to that point, voices of computers had been robotic and male. This is a tradition in Star Trek and a tribute to Gene Roddenberry's wife. Female voices are easier to understand and to listen to. Furthermore, a female voice in the ship may be based on older traditions and traits which would mean a woman’s voice might be considered to be sexier by Gene. 
Female voices are easier to understand and to listen to. A female voice in the ship may be based on older traditions and traits which would mean a woman’s voice might be considered to be sexier by Gene. 