"He is not fully ready yet and we feel that in a six-week tournament there is no need to press the issue right now," South Africa coach Ottis Gibson told reporters on Tuesday.
"He is getting closer every day. We hope that if not by Sunday (against Bangladesh) then by the India game."
Steyn, 35, was injured during the Indian Premier League and has not played since April 21.
He is considered South Africa's greatest fast bowler and returned to the one-day international team last November after two years on the sidelines with shoulder and foot injuries.
The Proteas have also had injury concerns over their two other main strike bowlers, Lungi Ngidi (side) and Kagiso Rabada (back), though both played in the warm-up win over Sri Lanka last week.
All-rounders Chris Morris and Dwaine Pretorius are in the frame to replace Steyn.
Fast bowler Anrich Nortje was ruled out before the tournament because of a thumb fracture sustained in training.
(Reporting by Nick Said; Editing by David Goodman)
