Hamilton, a six-time world champion who claimed the 90th 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.
The FIA had originally said it would consider the matter, but instead the FIA will clarify its guidelines on what will be allowed for drivers and teams both before and after the race.
The FIA aims to implement these guidelines ahead of the next race of the 2020 season, which will take place on September 27 in Sochi, Russia.
“I want you to know I won’t stop, I won’t give up, I won’t give up using this platform to shed light on what I think 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 just racial
“We can help make this a better place for our children and future generations.”
Taylor was shot and killed at her home in Louisville in March when three plainclothes police officers were carrying out an order.
“It has been six months since Breonna Taylor was murdered by police officers in her own home. Justice has still not been done. We will not be 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 wanted to wear that and raise awareness that there are people who have been killed in the street and there is someone who killed in her own house.
“We need to continue raising awareness … I think we should just get on with the matter.”
He has also announced plans to create a committee in his name to increase diversity in motorsport.
The win in the Tuscan GP means Hamilton is now one short of equaling Michael Schumacher’s record of 91 wins in F1.
DailyExpertNews’s Elizabeth Joseph and Susannah Cullinane contributed to this report.