Jones, who leads the Majors with a .395 batting average, was out of the lineup for a fifth straight game with a strained right quadriceps muscle and Yunel Escobar was removed from Wednesday's lineup when his strained left shoulder proved too sore during batting practice.
Both Jones and Escobar are hoping to return to the lineup for Friday's series opener against the Blue Jays in Toronto.
Jones has singled in the two pinch-hit at-bats he's collected in the past four games and then immediately been replaced by a pinch-runner. Although he's realized improvement, his leg still hasn't reached a point where he's completely confident he'll be able to run the bases while serving as a designated hitter this weekend against the Blue Jays.
"Any outfielder with any sort of arm could throw me out [at first base] right now," said Jones, who has shown a Kirk Gibson-like trot to first base after both of his singles. "I'm not trying to over-extend myself right now."
By the time next week arrives, Jones might not be the only familiar face Cox gets back into the mix. Although he went hitless in four at-bats in his first Minor League rehab appearance on Tuesday night, center fielder Mark Kotsay experienced no discomfort with his back.
Kotsay is expected to be activated when the Braves begin a three-game series against the Phillies next Tuesday. Over the next five days with Double-A Mississippi, he's expected to alternate on a daily basis as a center fielder and designated hitter.
"We're just going to ease him back into things," Braves general manager Frank Wren said of the veteran outfielder, who has been on the disabled list since May 26.
Joining Kotsay in Mississippi on Thursday will be infielder Martin Prado, who has been on the disabled list since May 5 with a badly sprained left thumb. Prado is expected to play six games and then be activated.
"That kid has really worked his tail off to get back," Cox said of Prado, who hit .282 in 18 games before suffering the thumb injury while sliding headfirst into first base.
In Wednesday's other injury-related news, Mike Hampton allowed two hits in 2 2/3 innings for the Gulf Coast League Braves. The southpaw, who reported no discomfort, was lifted when he reached his set limit of 45 pitches.
Wren says Hampton's final Minor League rehab appearance is currently scheduled for July 10.
If all goes well, that would put Hampton in line to join the Atlanta rotation after the All-Star break. But because he hasn't made a Major League start since 2005, it's tough to make any assumptions about his return.
"He hasn't had any discomfort," Wren said. "He's feeling good and we're hoping that continues to play out."