The 20-year-old world number 46 suffered the injury during her first-round victory over Italy's Romina Oprandi in the Qatar Open on Monday and returned home for treatment.
She was scheduled to participate in the Pacific Life Open in Indian Wells next week.
"She suffered a stretched anterior cruciate ligament injury in the right knee, which needs intense rehabilitation programme for at least four weeks," a hospital statement said.
Sania became her country's favourite sporting pin-up after she became the first Indian to claim a WTA title and crack the top-50 in the rankings.
Image: Sania Mirza with her mother at the Appollo Hospital in Hyderabad.
Text: Reuters | Photograph: Snaps India