Clarke missed his side's fourth and final Test against India earlier this week because of the problems, which Cricket Australia say are not new injuries, but an increase in the severity of previous issues.
"Michael Clarke had scans that confirmed his current lower back injury is an exacerbation of previous issues he has had with his spine," said chief medical officer Justin Paoloni.
"As always, we need to manage this carefully as there are potentially serious consequences with further aggravation.
"He still has pain with basic activities and is not back to full function as yet.
"He also has a hamstring injury that has been a concern for most of the summer and will complicate his return.
"Michael is having intensive rehabilitation for both his back and hamstring but is still 7-10 weeks away from returning to training and playing.
"We are confident that it will not affect his Ashes preparation but will know more over the coming weeks."
A 10-week absence would see Clarke returning at the start of June, with the first Test against England scheduled to begin on July 10.
The injury will likely rule him out of the whole of the upcoming Indian Premier League tournament for the Pune Warriors.
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