Clarke has been ruled out of the side's first Champions Trophy group match against England on Saturday due to injury, Cricket Australia said on Friday.
"Michael is making steady progress in his recovery from the recent lower back injury but is yet to return to training," Cricket Australia physiotherapist Alex Kountouris said in a statement.
"He will remain in London over the coming days to continue his rehabilitation and will not be available for the first match against England on Saturday."
Kountouris said the batsman's response to treatment would determine his availability for the match against New Zealand at Edgbaston on Wednesday.
Clarke is a key player for Australia, whose morale ahead of their title defence has already been dented by being bowled out for 65 by India in a warm-up match on Tuesday, and his absence will be a boost for hosts England.
The captain sat out that match in Cardiff after also missing last Saturday's encounter against West Indies.