Rahul, who captains Lucknow Super Giants in the Indian Premier League, tore a tendon in his right leg while fielding in the game with Royal Challengers earlier this week and limped off the ground.
"After careful consideration and consultation with the medical team, it's been concluded that I'll be undergoing surgery on my thigh shortly," the 31-year-old Rahul wrote on Instagram.
"My focus will be on my rehabilitation and recovery in the coming weeks. It's a tough call to make, but I know it's the right one to ensure a full recovery."
Lucknow, who made their debut last season in the world's richest cricket tournament, are second in the 10-team table with five wins from 10 matches.
Lucknow have named Karun Nair as Rahul's replacement in the T20 tournament, according to an IPL statement.
The injury also ruled out Rahul out of the WTC final against Australia from June 7-11.
"Absolutely gutted that I won't be at the Oval next month with Team India," Rahul said.
"I'll do everything I can to get back in blue and help my country. That has always been my focus and priority."
Rahul was included in the India squad, led by Rohit Sharma, despite his recent dip in form which saw him dropped from the XI for the final two Australia Tests.
Rahul, a wicketkeeper-batsman, has represented India in 47 Tests since his debut in December 2014, scoring 2,642 runs including seven centuries.
