"ogórka" - feminine noun, "-ego"
Oh please, stop confusing people.
Ogórek is definitely masculine.
The proper sentence should be:
"Ona ma jeden zielony ogórek" and this is how people would say that 20 years ago.
However, in today's Polish there is tendency to make some inanimate male nouns animate, and this is just one example of that.
So in the sentence: "Ona ma jednego zielonego ogórka" there's still Accusative, but ogórek is used as it was masc animate (not inanimate, as dictionaries still say).