Jones is expected to return in Week 5 for the Bengals' Oct. 5 against the New England Patriots. Cincinnati has a bye in Week 4.
The Bengals expect to keep Jones on the 53-man roster in the regular season and de-activate him in the three games before the game at New England. If for some reason they change their minds and want to place him on an injured reserve list, they have until Sept. 2 to make that decision.
On Monday, Bengals coach Marvin Lewis said the team expected Jones would be sidelined a "few weeks."
Jones had entered training camp as the No. 2 receiver on the depth chart, just ahead of Mohamed Sanu.
With Jones having missed nearly all of training camp with an ankle issue that he had just been cleared from last Monday, Sanu has taken his snaps and reps alongside A.J. Green.
The fracture occurred during Saturday's practice at Paul Brown Stadium. After the workout, Jones was seen in deep conversation with Lewis before walking slowly back toward the locker room. He had not played in Thursday night's preseason opener at Kansas City.
Jones, a third-year wideout, was Cincinnati's second-leading receiver in 2013, behind Green.
ESPN.com Bengals reporter Coley Harvey contributed to this report.