Maddon speculated that Price might miss "two or three" starts before he returns.
"And if that happens, I'm fine with that," Maddon said. "We have plans for playing in October. So we're not getting there without him. So if it takes an extra start to make sure he's well, that's fine."
To take Price's spot on the active roster, the club recalled Alex Torres from Triple-A Durham. The left-hander was available for bullpen duty Thursday night. A decision on who will make Price's start Monday afternoon in Toronto has not yet been made.
While there are obvious concerns in the Rays' camp about Price, a sense of relief countered that angst.
"I think we're very fortunate with the outcome of it," Evan Longoria said. "With pitchers' arms, you never know how bad it could be. So I think we got a pretty good break with the results of the testing. Hopefully we won't be without him for too long."
This is the first DL stint of Price's Major League career. The left-hander's start Wednesday against the Red Sox was cut short when he left the game in the third inning due to the injury.
"It's a new territory for me," Price said. "I've never really had any arm troubles. I missed a start last year because of my shoulder, but that was all done in the weight room and that all went away. This is frustrating, it is.
"I think it's even more frustrating because I'm throwing the ball as badly as I am. And that's when you really want to get back out there and get things going in the positive direction whenever anything is going bad. It's rough."
Price is 1-4 with a 5.24 ERA in nine starts this year. He did take some solace in the fact that the injury occurred earlier in the season rather than later.
"It's definitely good to have this come now as opposed to August or September," Price said. "Obviously every game is just as important as the ones that you play in April or May, but those are the ones that we put a lot of emphasis on because you're getting down to the end of the season and you're trying to make that playoff push and stuff like that. That's when you really want to be back for your team. I'll be back a lot sooner than that."
Price sounded optimistic about his forecast.
"We're just giving it some time to calm down," Price said. "That's really what we're doing right now. I feel pretty good today and I feel better than I felt when I left [Wednesday] night. So we're just giving it a little time to calm down and we'll be back out there in a couple of weeks."
Price felt like he could "throw right away," though he wasn't clear about what kind of timetable he will be on, nor did he know what his rehab stint will involve.
"I know I'm not going to be throwing for the next couple of days, but I feel OK," Price said. "We're just going to rehab it for a couple of days and go and throw a couple of [bullpen sessions] and just take it day by day, really."
Torres, 25, was 2-2 with a 2.39 ERA, 49 strikeouts, 14 walks and a .190 opponents' batting average in seven starts for Durham. He posted a 3.38 ERA over four appearances with the Rays in 2011, his only Major League action to date. Over eight Minor League seasons, the Venezuela native is 48-36 with a 3.59 ERA and 755 strikeouts.