Unlike with Neal, however, the Falcons expect Jones to return sometime this season.
"Following the game last Thursday, Deion reported soreness in his foot, so we sent him for further tests," coach Dan Quinn said in a statement. "We got the results of those tests back today, and he unfortunately will require a procedure that will result in us having to place him on injured reserve.
"We are bummed for Deion, but we do expect to get him back at some point this season. He represents all that we are looking for in a Falcon player, and while he will not be on the field for us right now, he will continue to have a presence in our building."
Each team is allowed to designate two players to return from IR each season.
Jones led the Falcons with nine tackles and had an interception in the 18-12 loss to the Eagles.
Jones and Neal were selected to the Pro Bowl in 2017, their second seasons in the NFL. Jones registered 138 tackles, three interceptions and a sack, while Neal had 113 tackles, three forced fumbles and an interception. Neal played the most defensive snaps for the Falcons last season while Jones played the third most.
Duke Riley could move into Jones' role at middle linebacker.
The Falcons also made practice squad moves Tuesday, promoting running back Brian Hill to the active roster. Receiver Julian Williams will take his place on the practice squad.
ESPN's Vaughn McClure contributed to this report.