St. Louis Public Radio reported the appeal was filed. No details were available.
U.S. District Judge Nanette Laughrey's stay came after Gov. Jay Nixon and the Missouri Supreme Court rejected attempts by Franklin's legal counsel to head off his execution, scheduled for 12:01 a.m. Wednesday.
Franklin and other death row inmates are challenging Missouri's execution method. He would become the first state inmate to be put to death under the new protocol, which has been changed several times from the three-drug cocktail used previously.
"While the facts have changed -- both in minor and significant ways -- there is clearly an overarching controversy concerning the department's method of execution," the judge wrote.
"Defendants [the state] cannot repeatedly change the execution protocol, including within five days of a scheduled execution, and rely on plaintiffs' lack of time to research the protocol's effects when arguing that plaintiffs have not presented a substantial likelihood of success on the merits.
"What research plaintiffs have produced in the little time afforded to them suggests a high risk of contamination and prolonged, unnecessary pain beyond that which is required to achieve death."
She said that means the inmates "have shown a significant possibility of success on the merits of their Eighth Amendment claim."
Nixon denied a clemency appeal by Franklin's attorneys.
Franklin was sentenced to death for using a sniper rifle to kill Gerald Gordon, 42, who was standing in a crowd of about 200 people outside a bar mitzvah ceremony at a St. Louis synagogue in 1977 that included his wife and three young daughters.
Twenty-two people died at Franklin's hands after he told investigators upon his capture he was trying to start a race war in America. Franklin also nearly killed Hustler magazine owner Larry Flynt on the steps of a Georgia courthouse because Franklin said he was angry over the magazine's depiction of interracial couples having sex. Flynt was severely injured and has been paralyzed ever since the attack.
Ironically, one of the legal challenges seeking to commute Franklin's death sentence was filed by Flynt, an ardent death penalty opponent. Flynt told CNN the legal appeal is a principled one not a personal one and he's overlooked his connection to the Franklin case.
Explaining his decision to deny the clemency, Nixon said Franklin's actions warrant capital punishment the St. Louis Post-Dispatch reported Tuesday.
"This cowardly and calculated shooting was only one of many senseless acts of extreme violence that Franklin, motivated by racial and religious intolerance, committed against numerous victims across the country," Nixon said in statement.