Hazlewood, who missed the second Test in Adelaide with a side strain, reported a calf issue before play Tuesday on the fourth day of the third Test, then bowled just one over before leaving the field.
"Josh Hazlewood has sustained a right-sided calf strain which will prevent him from playing any further part in the Test match against India in Brisbane," a Cricket Australia statement said.
"He sustained the injury during the warm-up this morning and after bowling one over was unable to continue.
"He is likely to miss the remainder of the Test series. A squad replacement will be made in due course."
The fourth Test begins in Melbourne on December 26 with the fifth and final Test in Sydney from January 3.
