No its not a common hindu female first name. Its not even a name.
The word you are looking for is "Shri"/"Shree"/"Sri" which is used as a prefix for the male name, like Mr., Mrs. etc.
As for being a word in South Indian languages... it's possible that it's an archaic word, but it's certainly not used commonly, at least in Kannada (which is my first language).
Anyway, my point is that it shouldn't have been there in the wikipedia page as a "common Hindu name", but I should probably be discussing this on the wiki talk page rather than HN. ;-)
"Siri, a common Hindu female name, meaning "Goddess Lakshmi, Wealth, God's gift of love."
http://en.wikipedia.org/wiki/Siri
Besides that, I know several Sikh women whose first name is Siri.
I do agree that Siri and Sri are the same, it's just a different way of spelling it.
Wikipedia simply points to a website full of names with no reference as to where they come from or statistics to back up the claim of it being common.