The returning paceman was ruled out of this week's Sophia Gardens clash and is only a slim chance of playing in the second match at Lord's because of an abdominal strain.
It is a serious setback for Ricky Ponting's men following Lee's stunning spell of reverse swing bowling last week against the England Lions at Worcester.
The New South Welshman had forced his way back into the Test side from ankle and foot surgery by displaying all of his old menace with a withering burst of 5-21 off 40 balls at New Road.
His ability to sharply reverse swing the ball in Worcester at speeds of around the 150km/h mark had been seen as a major asset for Australia with conditions expected to be similar in Cardiff.
Lee remained determined to return and play a role later on in the five-Test series.
"I'm gutted that I won't be there for that first Test match," he said.
"But I'll find a way to bounce back.
"I've gotten back from five ankle surgeries so I'm sure one little muscle strain won't keep me out for too long. " He backed Australia's pace attack that includes Mitchell Johnson, Peter Siddle, Stuart Clark and Ben Hilfenhaus to take care of business in Cardiff starting Wednesday.
"We've got a great bunch of guys, guys who are willing to go out there and do the hard work," he said.
"I've got the utmost confidence in the guys that they can do the job out there. " It is a particularly cruel blow for Lee after working his tail off to be in prime condition for Cardiff following ankle and foot surgery earlier this year.
But the 32-year-old said it wouldn't have been fair on his teammates if he had tried to play through the pain barrier in Wales.
"Normally I would have probably played through but with the summer we've got coming up, with the Test matches here and what it means to not only myself and to the team I didn't want to jeopardise that," he said.\
"But it's the start of the tour, it's happened now, it's before the first Test match so the guys can hopefully settle in and be one-nil up leaving Cardiff."
