Marrone also ruled out D.J. Hayden with a toe injury, marking the third straight game that the cornerback has missed.
Fournette aggravated his right hamstring during Sunday's 31-12 win over the New York Jets. The 23-year-old sustained 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 receive increased workloads in place of the 6-foot-1, 223-pound Fournette, who has rushed for 71 yards on 20 carries this season.
Yeldon had 18 carries for 52 yards and a touchdown and reeled in three passes for 48 yards and another score versus the Jets. Grant had five carries for as many yards and two catches for 12 yards.
Fournette led the Jaguars in rushing in his rookie season with 1,040 yards in 268 attempts and nine touchdowns in 13 games a year ago.
Jacksonville's first-round pick (No. 4 overall) in the 2017 NFL Draft, Fournette missed three games last year -- two due to an ankle injury and one game with a quadriceps injury.
Hayden, 28, has recorded eight tackles in two games since signing a three-year, $19 million contract in free agency to replace Aaron Colvin.