Kizer leads the NFL in interceptions this season.
The rookie quarterback also lost two fumbles in the game, Kizer only threw for 134 yards.
The Browns only had 50 rushing yards on the day.
Jaguars tight end Marcedes Lewis caught the first touchdown of the day.
Kizer threw a touchdown pass to Duke Johnson in the second quarter, it's his second touchdown catch of the season.
Cleveland is still looking for their first win of the season.
The Browns play the Cincinnati Bengals on Nov. 26.