Is there a Korean equivalent phrase if there is no exact translation?
Of course, "nunya" and "it's none of your business" are pretty impolite even in an informal setting, but should you wish to offend and defend, this is the way:
남이야 "nunya" (남이사 is a common colloquial variant)
상관하지 마 "none of your business"
너의 문제가 아니야 "it's not your problem"
Also, these are potential common phrases for such situations
몰라도 돼 "you don't need to know"
물어보지 마 "don't ask"
신경 쓰지 마 "don't worry about it"
These are not polite things to say, but
모르셔도 돼요 might pass for polite if said without "tone". And
신경 쓰지 않으셔도 됩니다 is okay even to your pastor or teacher, situationally, of course.
In addition to WEBjuju's answers, if you want to sound polite, you can say "제가 알아서 할게요" (I'll take care of it myself).
It's not always applicable, and in some situations it may still hurt the other person's feelings, but at least on the surface it sounds polite.
- NOTE: 할게요 must be pronounced as "할께요".
Just to add, a very strong but directly translated phrase is
"너 알 바 아니야." (pronounced as [너 알빠 아니야])
You should only use this phrase to friends, and only when you want to express anger or distress. However, as a native Korean, I think this is the most precise translation for 'none of your business.'