Williams and Ohanian's baby was born Sept. 1 in Florida.
"Dear mom," Williams wrote. "You are one of the strongest women I know."
"I was looking at my daughter [OMG, yes, I have a daughter] and she has my arms and legs! My exact same strong, muscular, powerful, sensational arms and body. I don't know how I would react if she has to go through what I've gone through since I was a 15 year old and even to this day."
I've been called man because I appeared outwardly strong. It has been said that that I use drugs [No, I have always had far too much integrity to behave dishonestly in order to gain an advantage]. It has been said I don't belong in Women's sports -- that I belong in Men's -- because I look stronger than many other women do. [No, I just work hard and I was born with this badass body and proud of it].
But mom, I'm not sure how you did not go off on every single reporter, person, announcer and quite frankly, hater, who was too ignorant to understand the power of a black woman."
Williams also explained that she is proud to be able to show the critics what some women look like.
"We don't all look the same," she wrote. "We are curvy, strong, muscular, tall, small, just to name a few, and all the same: we are women and proud!"
"Thank you for being the role model I needed to endure all the hardships that I now regard as a challenges--ones that I enjoy. I hope to teach my baby Alexis Olympia the same, and have the same fortitude you have had," Williams wrote.
Price has five children, including Serena and Venus. The Williams' father, Richard, has four children, including the superstar sisters.