Cashner is currently on the disabled list and receiving treatment for the injury. There's no timetable for his return, though it likely will exceed more than one month.
San Diego closer Huston Street missed 29 games with a similar strain and starting pitcher Eric Stults is currently on the disabled list with the same injury. Stults, who has missed 29 games, is scheduled to throw a simulated game on Saturday at Petco Park.
"I would suspect the same -- a month," said Padres manager Bud Black, who noted that Cashner will need at least a few Minor League rehabilitation starts before he returns.
Cashner left the game early against the D-backs on Tuesday after feeling pain while warming up for the bottom of the third inning. It was Cashner's second start since he moved into the starting rotation from the bullpen, where he was the Padres eighth-inning specialist.