Hawksworth did not pitch in 2012, undergoing three operations, two to his right elbow and one to his right shoulder.
The 29-year-old, obtained from St. Louis for Ryan Theriot two years ago, would have been eligible for salary arbitration this year if not outrighted to Albuquerque.
In 2011, Hawksworth pitched in 49 games for the Dodgers, going 2-5 with a 4.08 ERA.
Ken Gurnick is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.