Clarke missed the final Test of the 4-0 series defeat in India, as well as the IPL, due to back and hamstring problems.
He was not involved in Australia's first Champions Trophy warm-up against West Indies on Saturday, and the 32-year-old was also left out of the side to face India at the SWALEC Stadium today.
Cricket Australia has confirmed the skipper is a doubt for the clash with their Ashes rivals at Edgbaston.
Cricket Australia physiotherapist Alex Kountouris said: "Michael is still experiencing some lower back pain and as such is not fit for the warm-up against India today.
"Michael will head to London tomorrow for specialist treatment and a decision on his fitness for the next game will be made in due course."