The singer said she had the operation Wednesday, but she did not say at what hospital or when she expects to be discharged.
She canceled the rest of her Born This Way Ball Tour last week after suffering a labral tear of the right hip.
"Monsters, You really gave me a lot of strength today. Everything happened so fast, but when it came time to face it I reflected on the many stories and experiences you've shared with me about your lives," she wrote. "Meeting you backstage, reading your letters, watching you communicate with fans from around the globe to form a community that supports one another. You have completely blown my mind. As they wheeled me into surgery today, I thought about all of your pain and perseverance, your unique family situations, school environments, health issues, homelessness, identity struggles -- sometimes you are so brave that it terrifies me. I wonder how it's even possible. So I thought to myself, 'I'm alive, I'm living my dream, and this is just a bump in the road.' I'm grateful because this is temporary, and for some it is not. You have changed my life. I love you and am proud to be a part of your lives. If you can do it, I can do it too, and if we stick together we can get through anything."