The 35-year-old middle-order batsman said he would be available for selection and remain with the team, but was giving up the captaincy with immediate effect.
Rabada was in contention for selection as he worked his way back to fitness after a hamstring injury in June, but has been left out to continue his recovery.
World champion Lando Norris said Thursday that he believes McLaren can challenge for the podium again this week in Singapore after a difficult time in the last two races in Malaysia and Azerbaijan.
The world number three said his body was still adjusting to playing demanding matches after coming back from a wrist injury that sidelined him from April until the US Open in August.
Pakistan face Sri Lanka in a three-match T20 International series starting in Rawalpindi on Friday with all the matches will be held at the same venue.
