Escobar recorded a second-inning RBI triple in the contest. Diory Hernandez replaced him at the shortstop position when the bottom of the fourth began.
"I don't know if can play tomorrow," Cox said. "Now it's his back that is bothering him. I hope we can get him in there."
The Braves did not reveal how Escobar suffered the injury.
Escobar, who has produced a team-leading 44 RBIs, has battled a sore right hip flexor over the course of the past six weeks. It has not been revealed if Escobar has had any previous back ailments.
Mark Bowman is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.