Hamilton, a six-time Formula One champion who claimed the 90th race victory of his career on Sunday, wore a T-shirt with the words “ARREST THE COPS WHO KILLED BREONNA TAYLOR” in front and “SAY HER NAME” over a photo by Taylor on his back before the race and at the podium ceremony.
“The situation is under active consideration for a clarification that will be in place for the next race,” an FIA spokesman told CNN.
The spokesman did not confirm which rule Hamilton will be investigated for breaking.
Taylor was fatally shot at his home in Louisville in March when three regular police officers executed a “no-knock” order.
“It’s been 6 months since Breonna Taylor was murdered by police in her own home. Still no justice has been done. We do not remain silent,” Hamilton posted on Twitter along with photos of himself wearing a T-shirt.
He also added in a post-race conference: “It took me a long time to get that jersey and I wanted to wear it and bring attention to the fact that there are people who have been killed on the street and there are some who was killed in her own house.
“We have to keep raising awareness … I think we’ll just have to keep pushing the issue.”
Victory at the Tuscan GP means Hamilton now needs to match Michael Schumacher’s record of 91 race victories in F1.
He has also announced plans to set up a commission in his name to increase diversity in motorsport.
CNN’s Elizabeth Joseph and Susannah Cullinane contributed to this report.