"Three to six weeks is just a guesstimate," Cashman said. "It could be longer. Nobody's told me about season-ending, but at the same time, he's going to be ready when he's ready."
The tear is not expected to require surgery and was believed to have been suffered on Tuesday at Rogers Centre in Toronto, as Giambi ran out a home run to left-center field off the Blue Jays' Scott Downs.
Giambi -- who stole a base earlier in the game and advanced to third on an error -- appeared to limp noticeably after rounding the second-base bag and gingerly completed his trip around the bases. He later admitted that he'd felt a "pop."
"When you heard that, you knew something wasn't right," Cashman said.
"I saw the Babe Ruth look there when he was running around the bases," Yankees manager Joe Torre said. "He was in a great deal of pain."
Giambi has been placed in a walking boot, and the Yankees officially placed Giambi on the 15-day disabled list prior to Friday's game at Fenway Park in Boston, where the club opened a three-game series with the Red Sox.
Giambi had been noticeably hobbled by pain in his left foot for the better part of two weeks, which has limited his ability to push off while batting because the injury affects his back, or plant, foot.
"[Losing Giambi] hurts, but he's been playing with that bad foot for a period of time, and he hasn't been able to be the same hitter that we all know," Cashman said.
During the Yankees' three-game series in Toronto, Giambi successfully lobbied the training staff to allow him to return to New York in hopes of receiving a cortisone injection in the heel of his foot, which Giambi thought would permit him to quell the pain for the series against the Red Sox.
"I do fine for one day, and then I struggle for three," Giambi said on Tuesday. "We obviously need me to be that player that I am, where I can help carry the team. Singles aren't really going to get it done. I've got to be able to drive the ball."
Instead, a precautionary MRI revealed the injury to Giambi's plantar fascia, which Cashman said was not in the original examinations and did not show a complete tear.
Yankees outfielder Johnny Damon said he learned of Giambi's status while watching the news ticker crawl across a television channel.
"It wasn't what we were expecting," Damon said. "If we would have known, we would have just had him fly to Boston with us."
In 45 games for New York, Giambi is batting .262 with seven home runs and 23 RBIs. He batted just .172 (10-for-58) in his injury-marred May.
Cashman said that Giambi will not travel on the road with the club, as he has been instructed to remain in New York and begin the healing process.
"It doesn't make sense to have him on the road," Cashman said. "He'd want to be with the club to root them on and all that stuff, but there's no treatment. All he has to do is wait."
In Giambi's absence, the Yankees plan to use Melky Cabrera as a regular player in the outfield while allowing Damon to serve as a designated hitter for the majority of the time, so he can get more mileage from his aching body.
"You certainly don't want to deal without Jason, but he was in and out, and when he was in, he was hurting," Torre said. "This may be a blessing in disguise. We know who we have and we know what we're going to do."