"Two or three days," Braves manager Bobby Cox said when asked how long his third baseman might be out.
Jones, who has been plagued by oblique issues in recent years, wouldn't put a timetable on his return.
"It's taken two or three days to three or four weeks," Jones said of his past problems. "We've done all we can [this time] to get it on its way [to healing] and we'll just have to wait and see."
Jones was replaced by Omar Infante at the start of the fourth inning after two painful swings in the bottom of the third.
"I couldn't push it any further," he said.
The 2008 National League batting champion first experienced problems at the end of batting practice but decided that he would try to play.
"I tweaked it the second-to-last swing of BP and made it worse the last swing," Jones said. "I hoped that it would loosen out, but it didn't. I felt OK my first time up."
But Jones grimaced noticeably while batting in the third inning, then ran the bases gingerly after drawing the walk.
The switch-hitter spent time on the disabled list with an oblique strain in 2006 and has been bothered by side issues at times ever since. "I think I've strained every muscle I've got," he said.
The oblique strain came the day after Jones won a game for the Braves with a homer, his two-run blast in the eighth inning producing a 3-2 victory over the Cubs. It was the 427th homer of his career and tied Mike Piazza for 39th on the all-time list.
"To be honest, it never gets old," Jones said of the game-winning homer. "It felt good and it's nice to get the first one out of the way early instead of having to wait a couple of weeks."
Guy Curtright is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.