The Windies leg-spinner had injured himself during the World Twenty20 final on April 3 and has not played a game since then.
He will be replaced by chinaman bowler Tabraiz Shamsi, who plays for South African franchise Titans.
Shamsi, 26, previously played in the Caribbean Premier League (CPL) after catching the eye of the touring West Indies in South Africa in 2014-15.
He enjoyed reasonable success at the CPL, claiming 11 wickets in seven games at an average of 13.27 for St Kitts and Nevis Patriots in 2015.
RCB have lost two of their three matches so far and their bowling has been mediocre. They do not have a go-to bowler who can either stem the flow of runs or fetch wickets. Mitchell Starc or Samuel Badree could have played that role. But without them, the bowling is without a rallying point.
Shamsi tweeted his happiness at being picked for RCB for the rest of the IPL season.
— Tabraiz Shamsi (@shamsi90) April 21, 2016
(With inputs from agencies)