Putz, who converted 40 of 42 save opportunities last season, and was selected as the American League's Rolaids Relief Man Award winner, registered a save against the Rangers on Opening Day, pitching a scoreless ninth inning, and went for another one the following night at Safeco Field.
But when he threw a split-finger fastball that struck out Michael Young, Putz felt a sharp pain in his left side, which he described as, "an ice pick stabbing me in the side."
Josh Hamilton hit Putz's next pitch for a two-run home run that gave Texas a 5-4 victory.
An MRI exam after the game revealed that Putz had the injury, officially known as "costochondritis."
He was placed on the 15-day disabled list the following day, and will be eligible to be activated on April 16.
Griffin never predicts when a player might return to action, and he refused to speculate on when Putz might be able to pitch in a game again.
"You have to judge what they do, based on how they feel," Griffin said. "You have to listen to their body. He has to be very honest, and he will be. J.J. understands the consequences of not being honest. You can't trick this injury."
The Mariners' bullpen has faltered since Putz's departure.
While the starting rotation has done its job early the season, compiling a 2.66 ERA through the first seven games, the 'pen has been hit hard. Going into Tuesday night's series opener against the Rays, the Mariners' 8.04 ERA as a relief corps ranked 30th -- last -- in the Majors.
But help could be on the way before too long.
Left-hander Arthur Rhodes was sent to Double-A West Tennessee on Tuesday to continue his work, and right-hander Brandon Morrow, already with the Double-A club, pitched two scoreless innings on Monday night. He surrendered one hit, walked three, struck out four and uncorked a wild pitch.
Both would be eligible to join the Mariners on Thursday, the day before Seattle opens a three-game series against the AL West rival Angels at Safeco Field.
"Everything is very positive with both of them," manager John McLaren said. "We like what we're hearing."