Zimmerman was on trial for the second-degree murder of 17-year-old Trayvon Martin and pleaded not guilty, claiming self-defense.
He was found not guilty by a Florida jury last weekend.
The petition, addressed to the Obama administration, reads:
Petition Requesting Prosecution of George Zimmerman for depriving Trayvon Martin of his Constitutional Rights of Life and Liberty by the United States Department of Justice, Eric Holder, United States Attorney General in United States District Court as swiftly and expeditiously as is possible.
The petition has racked up 31, 367 votes as of Wednesday night, requiring 68,633 additional signatures by August 13 to meet the goal of 100,000 signatures.
A similarly-themed NAACP petition has already drawn more than 1 million supporters.
Follow Carrie Healey on Twitter @CarrieHeals.