Jones, who had not played since May 24 against the New York Mets, initially bruised both hands in a May 11 collision with Pittsburgh third baseman Jose Bautista. He missed four games and then returned to play in the next seven.
"Now he just can't play," Manager Bobby Cox told The Atlanta Journal-Constitution. "It's been eight days and (the right hand) hasn't gotten any better."
The move is retroactive to May 24.
"The frustrating part of this is I have seen no improvement whatsoever," Jones said on Atlanta's Web site.
Multiple leg and foot injuries have prevented him from playing in more than 110 games either of the past two seasons. He is batting .300 with 12 home runs and 27 RBI in 160 at-bats, with a .600 slugging percentage.
Atlanta recalled third baseman Yunel Escobar from Class AAA Richmond.