Rizwan and Irfan both suffered hamstring injuries in the third match in Rawalpindi, where a second-string New Zealand side won by seven wickets to level the five-match series 1-1
In a statement posted on social media, Punjab Kings said the 29-year-old Indian batsman was transferred to a hospital after he complained of severe abdomen pain on Saturday night and did not respond to medication.
"He (Rahul) was taken to the emergency room for further tests which revealed that he was diagnosed with acute appendicitis," Punjab Kings said in a statement.
"It will be resolved surgically and for safety measures he has been transferred to the hospital for the same."
Rahul is the top run-scorer of the IPL 2021 season, recording 331 runs in seven matches with four half-centuries.
Punjab Kings, who face second-placed Delhi Capitals later on Sunday, are currently fifth in the league table with three wins from seven matches.