Wahab suffered a tournament-ending ankle injury during Pakistan's crushing 124-run defeat by title-holders India in their opening match at Edgbaston on Sunday.
Rumman, also a left-arm fast bowler, has represented Pakistan in two Twenty20 Internationals to date.
The 25-year-old has also taken 123 wickets in 42 first- class matches.
But Pakistan captain Sarfraz Ahmed indicated Junaid Khan, already with the squad, would replace Wahab for his side's second Group B fixture against South Africa at Edgbaston on Wednesday.
A miserable match for Wahab, flayed for a hugely expensive 87 runs in 8.4 overs, ended when he fell in his delivery stride and sustained an injury that saw him leave the field.
It also meant he was unable to bat as Pakistan, chasing a revised target of 289 in 41 overs in a rain-affected match, slumped to 164 for nine after India had piled up 319 for three.
Junaid was left out of the clash with arch-rivals India despite taking four for 73 in a warm-up match against Bangladesh.
The Pakistanis conclude their group campaign against Sri Lanka in Cardiff on June 12.
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