Ivey, a Republican, made her apology after an audio tape emerged of a 1960s radio interview she and her then fiance, Ben LaRavia, gave when she was a student at Auburn University in Alabama.
In the interview, LaRavia described a recent comedy sketch they had been in.
"As I look at my fiancée across the room I can see her that night, she had on a pair of blue coveralls and she had put some black paint all over her face and we were acting out this skit called 'cigar butts,'" LaRavia said in the interview.
Ivey, 74, who is white, said in a statement on Thursday she does not remember the skit but that, based on the radio interview, it would have occurred at a Baptist Student Union party.
In her statement, Ivey said, "I fully acknowledge - with genuine remorse - my participation in a skit like that back when I was a senior in college." "I offer my heartfelt apologies for the pain and embarrassment this causes, and I will do all I can - going forward - to help show the nation that the Alabama of today is a far cry from the Alabama of the 1960s.
We have come a long way, for sure, but we still have a long way to go."