He was India captain Rohit Sharma's opening partner in the home T20 series against Afghanistan earlier this year but his place looked under threat as he struggled for runs in the IPL
"Mohammed Shami got (a) mild left knee problem and had ultrasound guided injection yesterday," a statement on the ICC's World Cup website said.
"For his long-term management perspective he won't be available for Saturday's match against UAE."
The 24-year-old had taken a total of six wickets from India's opening wins over Pakistan and South Africa.