As far as I know, it is the only word where wo is pronounced as wee. What is the reason for this? Does it have to do with the origin of the word?
Well, here in the Midwest of the US, we don't pronounce it 'wee'.
In the singular form, 'woman', we use a sound similar to the word "wool". The IPA is: `wʊ̈-mən.
In the plural form, 'women', we use the pronunciation that RedDwight has in his answer, with a sound similar to the word 'it' or 'win'. The IPA is: `wɪ-mən.
So, in neither case does a long "e" sound.
I was prompted to reopen this question by the appearance of this very similar question Why is “women” pronounced as wimin?
Further to the answer by RegDwigнt (Nov 4 '10 at 9:55), I find that reply unsatisfactory in a couple of respects.
1. Examine the following from Etymology Online:
That makes no sense. If woman means woman-man then perforce woman-man means woman-woman-man and woman-woman-man means woman-woman-woman-man.
2. We are also told:
This is a non-explanation. Why doesn't the rounding influence of -w- also affect the plural?
My tentative answer
Given that the question is 'What is the reason for this?' I think more explanation is needed.
Here is a partial explanation that I put forward as a hypothesis.
Given the Old English words O.E. wimman (sing.) and wimmen (pl.) we can say the following.
At the time those words were in common use, the majority of people were illiterate, they wouldn't have been aware of spelling differences. They would have spoken and heard the words only.
With the transition from OE to ME there would be a tendency, as in modern English, for the words to be stressed on the first syllable and for the final syllable to degenerate towards a neutral or schwa sound. If that happened then both would have /mən/ as the final sound regardless of the pronunciation of the first syllable.
In other words the two would sound identical wimmən (sing.) and wimmən (pl.)
Now these words would have been in common daily use and it would have been intolerable to be unable to distinguish between singular and plural. It would also have been uncomfortable and unnatural to always clearly enunciate the second unstressed syllable.
I therefore suggest that a difference in the sound of the first syllable was bound to evolve. The fact that the plural version retained the original sound (from wifman) and the singular version moved away from it was arbitrary. It could have worked the other way around.
We could bring in here the 'rounding influence of -w-' and hazard that the singular word was commoner and therefore more susceptible to the rounding effect. The plural would then keep its original form simply out of necessity.
If that is what was meant by Etymology Online then all well and good.
I am not an authority on Old English or Middle English or their pronunciation. My answer has at best the status of an educated guess.
I have given it to move things forward because I don't believe any of the other answers so far have addressed the heart of the matter.
If anyone can prove me wrong then I shall be as interested as if I can be proved right.