Jones is scheduled to rejoin live batting practice on Thursday.
"We'll get him involved in that, get him to move around a little more," manager Clint Hurdle said. "We'll see where that takes us, but he's definitely moving forward."
Jones was 3-for-14 in six games prior to his setback.
Tom Singer is a reporter for MLB.com and writes an MLBlog Change for a Nickel. He can also be found on Twitter @Tom_Singer. This story was not subject to the approval of Major League Baseball or its clubs.