Rabada will miss the short-format matches that will be played in Bristol on Wednesday and Friday after being diagnosed with a left medial ankle injury.
According to a statement by Cricket South Africa (CSA), the paceman "will continue medical management and rehabilitation" and "will be closely monitored in preparation for the upcoming three-match Test series against England later this month".
The highly-anticipated Test series against Ben Stokes' side kicks off at Lord's on 17 August followed by games at Old Trafford and the Oval.
The 27-year-old Rabada was rested was for the three ODIs against England at the start of the UK tour before returning for the first two T20 matches.
He then sat out the series-winning game in Southampton on Sunday with what was described as a "niggle".
The Proteas squad are on high after thumping England by 90 runs at the Ageas Bowl and will look to continue that good form against the Irish in Bristol.