Hamilton, a six-time world champion who claimed the 90th race win of his career on Sunday, wore a T-shirt with the words “ARREST THE COPS WHO KILLED BREONNA TAYLOR” on the front, and “SAY HER NAME” above a photo of Taylor on the back, before the race and at the podium ceremony.
Having originally said it would be considering the matter, the FIA will instead clarify its guidelines as to what will be permitted for drivers and teams both pre and post-race.
The FIA is aiming to put these guidelines in place ahead of the next race of the 2020 season which is scheduled to take place in Sochi, Russia on September 27.
“Want you to know I won’t stop, I won’t let up, I won’t give up on using this platform to shed light on what I believe is right,” Hamilton wrote on Instagram.
“I want to thank those of you who continue to support me and show love, I am so grateful.
“But this is a journey for all of us to come together and challenge the world on every level of injustice, not only racial
“We can help make this a better place for our kids and the future generations.”
Taylor was fatally shot in her Louisville home in March as three plainclothes police officers executed a “no-knock” warrant.
“It’s been 6 months since Breonna Taylor was murdered by policemen, in her own home. Still no justice has been served. We won’t stay silent,” Hamilton posted on Twitter on Sunday, alongside photos of himself wearing the T-shirt.
He also added in a post-race conference: “It took me a long time to get that shirt and I’ve been wanting to wear that and bring awareness to the fact that there’s people that have been killed on the street and there’s someone that got killed in her own house.
“We have to continue to raise awareness … I think we just have to continue to push on the issue.”
He has also announced plans to set up a commission in his name to increase diversity in motorsport.
Victory at the Tuscan GP means Hamilton is now one short of equaling Michael Schumacher’s record of 91 race wins in F1.
CNN’s Elizabeth Joseph and Susannah Cullinane contributed to this report.