Cricket South Africa has advised Rabada, who has taken 25 wickets in 12 games for the Delhi Capitals, to return home as a precaution, the IPL team said.
He is just the latest South African bowler to suffer an injury scare after Dale Steyn lasted only two IPL games before withdrawing with a shoulder problem.
"It is indeed very hard for me to leave the Delhi Capitals at this stage of the tournament," Rabada said in a team statement.
"But with the World Cup just a month away, a collective decision has been made for me in this regard.
"It's been a tremendous season for me with the Delhi Capitals, both on and off the field, and I truly believe that our team can win the trophy."
Fellow South African quicks Lungi Ngidi and Anrich Nortje also skipped the IPL to deal with injuries. The World Cup in England and Wales starts on May 30.
Rabada is leaving with Delhi already qualified for the IPL playoffs. Their final league game is against the Rajasthan Royals on Saturday.
"It's unfortunate that Rabada is having to leave us at this stage of the tournament," said Capitals coach Ricky Ponting.
"But I have full confidence in our team, and I'm sure each and every member of this unit will step up to the occasion."