There's no timetable for Jackson's return, said Padres assistant general manager A.J. Hinch.
Greene was hitting .200 in 41 plate appearances this season for Gwinnett. He's a career .224 hitter in parts of five big league seasons with the Cardinals, Astros and White Sox.
Greene hit 11 home runs in a combined 330 plate appearances with the Cardinals and Astros in 2012.
Greene appeared in 10 games at shortstop with Gwinnett and that's his primary position, although he can also play second base and third base.
Greene was the 30th overall pick by the Cardinals in the 2005 Draft out of Georgia Tech.
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter. This story was not subject to the approval of Major League Baseball or its clubs.