The Jaguars will try to win consecutive games for the first time this season when they host the Cincinnati Bengals on Sunday.
Both players received personal foul penalties and were ejected.
Ramsey and Green had been trash-talking throughout the first half, and things came to a head after a running play with less than 30 seconds to play. When the fight broke up, Green threw his helmet off on the field and walked straight to the Bengals' locker room. Green had 38 catches for 572 yards and four touchdowns coming into the weekend.
Fournette is sixth in the National Football League in rushing thus far in 2017 with 596 yards rushing in just six games.
Earlier this year, Green said of his subdued nature: "That's who I am".
The Jacksonville Jaguars have a very simple formula for winning games - run the ball effectively and play great defense - but they struggle to put those things together with consistency.