The 29-year-old, who scored 180 in Australia's last test against Sri Lanka in February, left his English county side Lancashire for "personal reasons" after making just one appearance for the club.
Queensland Cricket said he had undergone tests since returning to Australia and been diagnosed with a "protracted post-infectious fatigue disorder dating back to an October 2018 viral infection."
"Joe is currently undertaking a treatment period of rest and recuperation," QC CEO Max Walters said.
"A definite prognosis for recovery is unavailable at present; however it is anticipated he will be fully available for cricket in the near future."
The 16-test opener has scored four centuries but been in and out of the test side since his 2014 debut against India in Melbourne.
He is vying with Marcus Harris, Usman Khawaja and David Warner for a top-order spot in Australia's squad for the Ashes series starting on Aug. 1 in Edgbaston.
(Reporting by Ian Ransom; Editing by Peter Rutherford)
