Marrone also ruled out nickelback D.J. Hayden with a toe injury, which is a significant loss as well because of the Chiefs' high-powered pass offense.
Fournette aggravated a previous injury to his right hamstring during the team's victory over the New York Jets last Sunday. He suffered the original injury in the first half of the season opener against the New York Giants.
Running backs T.J. Yeldon and Corey Grant will get the bulk of the work in Fournette's place. Yeldon ran 18 times for 52 yards and a touchdown and caught three passes for 48 yards and another touchdown against the Jets. Grant had five carries for 5 yards and two catches for 12 yards.
Brandon Wilds, whom the team elevated from the practice squad two weeks ago, is the only other running back on the active roster. The team worked out Orleans Darkwa and Matthew Dayes on Tuesday but did not sign either.
Fournette had an MRI on Sunday following the Jaguars' 31-12 victory at TIAA Bank Field, and Marrone said the injury did not appear to be more serious than it was when he first hurt his right hamstring late in the first half of the season opener. Marrone said Fournette feels a "catch" in the hamstring when he tries to accelerate to top speed.
Earlier this week, Marrone said he had no idea how long Fournette could be out.
"We'll just take it day by day," he said.
The Jaguars play at Dallas on Oct. 14 before playing host to Houston the following Sunday and then traveling to London for the team's annual home game in Wembley Stadium. The Jaguars have their bye the following week, so it's not out of the question that Fournette could be held out until their Week 10 game at Indianapolis on Nov. 11.
Fournette ran 11 times for 30 yards and caught one pass for 5 yards before going to the bench late in the first half against the Jets. The team originally said he was questionable to return, but he went back onto the field for the Jaguars' final drive of the half. The team ruled him out for the second half.
Fournette missed the Jaguars' games against New England and Tennessee with the initial injury.
This will be the third game in a row that Hayden, who signed a three-year, $19 million contract in free agency to replace Aaron Colvin (who signed with Houston), has missed with the toe injury. He suffered the injury when someone stepped on his foot during a light Friday workout before Week 3.