However, photos of Shiloh, 13, have captured her walking around on crutches this week suggesting she may have had the surgery, and not Vivienne, 11.
She added that her children encouraged her to write the article about them.
"I have spent the last two months in and out of surgeries with my eldest daughter and days ago watched her younger sister go under the knife for a hip surgery," Jolie wrote in her essay.
"They understand that going through medical challenges and fighting to survive and heal is something to be proud of.
"I have watched my daughters care for one another. My youngest daughter studied the nurses with her sister and then assisted the next time."
She said she saw how easily her daughters dropped everything to put each other first.
"I also watched them face their fears with a resolute bravery."
The actress said her sons, Maddox, 18, Pax, 16, and Knox, 11, were "supportive and sweet" towards their sisters and were there for them through rough times.
At the end of her essay, she encouraged young girls to "fight on" and "know their rights".
On Sunday, Jolie was pictured in public with Shiloh, who was seen using crutches, and Vivienne.
The actress has six children with ex-husband Brad Pitt, whom divorcd after more than 10 years of being together and a year after of marriage.
