Johnson, signed in the offseason to a one-year free agent contract, had a right forearm strain in spring training. The right-hander was placed on the 15-day disabled list March 29, retroactive to March 21.
''I don't know if you'd call it a setback, he just hasn't gotten better,'' Padres manager Bud Black said Tuesday. ''There's probably more tests and more evaluations (coming).''
The initial prognosis was that Johnson was due to be out about one month. But his lack of progress makes that time frame unlikely and has the club concerned he may be out for much longer.
Johnson underwent surgery on his right elbow to remove bone spurs during the offseason.
Johnson has a history of arm issues, most notably Tommy John surgery in 2007.