Shahzad, who took five wickets on debut in the 360-run loss to the hosts in Perth, had complained of discomfort in his left side during the series opener and was taken for a scan.
The Pakistan Cricket Board (PCB) said it had found a stress fracture in a left rib along with the muscle tear.
"PCB will now consult a specialist in Australia after which a final management protocol will be established for the player," the PCB said in a statement.
Shahzad's injury is another blow for Pakistan ahead of the second test at the Melbourne Cricket Ground, which starts on Tuesday.
Captain Shan Masood's side are already depleted in attack, with injured quick Naseem Shah sidelined and Haris Rauf having opted out of the series to play in Australia's T20 Big Bash League.
