The team noted on its Web site Thursday night that the veteran slugger aggravated the injuries in Wednesday night's game against the New York Mets.
A second opinion Thursday verified his suspicions.
He initially hurt himself in a May 11 collision with fellow third baseman Jose Bautista of Pittsburgh and a subsequent tumble on the same play.
"I came in (to the doctor Wednesday night) and said, 'This needs rest,'" Jones said. "It's not getting any better. If anything, it's getting worse."
Jones missed Thursday night's series finale.
He has a .300 batting average with 12 home runs and 27 RBI this season.