The Queenslander called time on his stint with Lancashire last month for "personal reasons".
Queensland Cricket said in a statement he was dealing with "a protracted post-infectious fatigue disorder dating back to an October 2018 viral infection".
Burns, who has played 16 Tests and was a contender to open with David Warner at the year's Ashes, is recuperating.
"A definite prognosis for recovery is unavailable at present; however it is anticipated he will be fully available for cricket in the near future," added the statement.
Whether he recovers in time for the first Test at Edgbaston on August 1 remains to be seen, but his problems could open to door for Marcus Harris or Cameron Bancroft.
Coach Justin Langer told reporters it would be tough to select Burns, given how much county cricket he will miss.
"He's one player we were hoping would play six, seven, eight games of red-ball cricket," he said.
"That was the plan initially. Sometimes plans change, and we'll just have to monitor that over the next a little bit."
Burns was replaced in the Lancashire squad by fellow Australian Jake Lehmann, son of former national coach Darren Lehmann.