Johnson is scheduled to start on Thursday night for Triple-A Tucson, and Arizona manager Bob Melvin said that Johnson is likely to make one more Triple-A start on April 8.
With next Thursday's off-day, each starter will get an extra day of rest, so that would mean Johnson would start on April 14 in place of Doug Davis, who will undergo surgery to remove a cancerous thyroid on April 10.
Johnson underwent surgery on his back for the second time in two years last August and was about two weeks behind the Diamondbacks' other pitchers this spring. The big left-hander is in the final year of his contract and is 16 wins away from 300 for his career.
Steve Gilbert is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.