Hamilton, a six-time Formula One 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.
“The situation in under active consideration for a clarification that will be in place for the next race,” a spokesman for the FIA told CNN.
The spokesperson did not confirm what rule Hamilton will be investigated for breaking.
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 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.”
Victory at the Tuscan GP means Hamilton is now one short of equaling Michael Schumacher’s record of 91 race wins 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.