ESPN's Adam Schefter reported the news, noting the Falcons' upcoming bye week will help give Jones time to recover. The Pro Bowler had three receptions for 30 yards before exiting in the second quarter.
Falcons coach Dan Quinn told reporters Jones wanted to return to the game but was held out.
"He had trouble just exploding, and if he can't be him, that's a unique thing for him," Quinn said. "The speed, the explosiveness—so when he wasn't able to do that, that's when we had to pull him. He definitely wanted to go."
The Falcons also lost wideout Mohamed Sanu to an injury.
Jones, 28, has missed at least one game in four of his previous six seasons. He missed two games in 2016 but still finished with 83 receptions for 1,409 yards and six touchdowns.
If Jones' prognosis winds up being worse than the team thought, Sanu (if healthy) and Taylor Gabriel should see additional targets.