"It's just a tweak," Jones said in a message to reporters relayed through Braves spokesman Brad Hainje.
Jones hopes to play on Wednesday, but he could be held out at least another 10 days.
Jones, whose 35th birthday is next month, said his absence from the lineup is "precautionary, to make sure it's 100 percent."
Jones was pulled out of Friday night's game after feeling the soreness in his right side during batting practice.
The injury caused alarm because Jones missed a combined total of 27 games with two trips to the disabled list because of a strained left oblique last season.
Braves manager Bobby Cox has taken a cautious stance on Jones' injury. On Friday, Cox proclaimed he'd protect Jones for the season "if it takes the rest of spring." Cox shifted from that stance only slightly on Sunday.
"Chipper is a little better today," Cox said. "He's looking at Wednesday. We'll see."
BRAVES (SS) 4, TIGERS 3
KISSIMMEE, Fla. - Brandon Jones hit a two-run homer and Brian McCann added a long shot over the right-field bullpen to lead the Atlanta Braves past the Detroit Tigers 4-3 in a split-squad game Sunday.
Atlanta's Tim Hudson walked one and gave up three hits in five scoreless innings.
BRAVES (SS) 6, REDS 5
SARASOTA, Fla. - Jeff Francoeur hit a two-run homer and Kelly Johnson added a solo shot to lead the Atlanta Braves past the Cincinnati Reds 6-5 in a split-squad game Sunday.
Buddy Carlyle limited the Reds to four hits over four innings. Carlyle, who picked up the win, gave up no runs, struck out four and left with the Braves ahead, 4-0.
- Associated Press