Williams wrote about her nephew taking her to meetings when she noticed a police officer on the side of the road.
"Today I asked my 18 year old nephew (to be clear he's black) to drive me to my meetings so I can work on my phone #safteyfirst. In the distance I saw cop on the side of the road. I quickly checked to see if he was obliging by the speed limit. Than [sic] I remembered that horrible video of the woman in the car when a cop shot her boyfriend. All of this went through my mind in a matter of seconds. I even regretted not driving myself. I would never forgive myself if something happened to my nephew. He's so innocent. So were all 'the others.'"
Williams' post referenced the death of Philando Castle, the 32-year-old shot and killed by police in Falcon Heights, Minnesota.
Castile was killed in a traffic stop on July 6 after he informed the police officer that he was carrying a gun. Cellphone video taken by his girlfriend, Diamond Reynolds, showed Castile sitting in the driver's seat of the car with a shirt that appears to be soaked in blood. The officer can be heard saying, "I told him not to reach for it. I told him not to get his hand out."
Williams continued in her post, saying she believes while there are ignorant and insensitive people, not "everyone is bad."
"I am a total believer that not "everyone" is bad. It is just the ones that are ignorant, afraid, uneducated, and insensitive that is affecting millions and millions of lives.
Why did I have to think about this in 2016? Have we not gone through enough, opened so many doors, impacted billions of lives? But I realized we must stride on- for it's not how far we have come but how much further still we have to go."
The tennis star then, quoting Dr. Martin Luther King, wrote she does not want to be silent.
"I than wondered than have I spoken up? I had to take a look at me. What about my nephews? What if I have a son and what about my daughters? As Dr. Martin Luther King said, "There comes a time when silence is betrayal."
In just three hours, her Facebook post has been shared more than 6,000 times.
ABC News contributed to this article.