Tonight I had to deal with this very problem, BUT, I was the one that had stuffed up and said something I should not have. This is a very close friend of mine, and I had shared some information that she had told me, and I was upset I had over stepped the boundries of our friendship, and knowing how important she is to me, I knew I had to come clean and tell her what had happened, why, and that I was sorry, and I knew that I was in the wrong. This is what I did......
I texted her during the day asking her to meet up with me later in the day, as I felt I had made a mistake, and over stepped boundries at her engagement party. (I did this text for two reasons, one, so I had to go through with this tough talk with her, and two, to give her some warning). We texted back and fourth a bit, and all the time, I made it clear to her, that I was in the wrong, that I needed to face what I had done, and she may be angry with me, but that I was willing to risk that, as long as I was up front with her, and she knew my intention was to cause no malice.
We meet up as arranged, I came clean, told her from beginning to end what had happened, and to my relief, I had not betrayed her at all, the other person already knew what I had said.
It was a tough thing to do, but the lessons learn't are valuable, I learn't my friend is forgiving and understands that I am hard on myself when I think I have hurt someone I care about, that we can be open with each other, and honestly look at a problem without fear of braking up our valued relationship. She learn't that when I have done something that is not true to myself, I will go and tell her, that I am up front, and I care about her enough that I will be honest with her, even when I have done the wrong thing.
I suggest you do have a talk with your friend, look at the problem, lay it all on the table, be honest with each other, and new understanding and lessons may be learn't on both sides. None of us are perfect, we all make mistakes - there are two kinds of mistakes, the ones we do on purpose to hurt another, and the ones we do by accident without meaning to hurt each other. Good luck