Manjezi suffered the injury in their first of two Guinness PRO14 derbies against the Isuzu Southern Kings, which saw him miss the return match in Bloemfontein last week.
He will join Craig Barry (winger), Gerhard Olivier (looseforward) and Reinach Venter (hooker) as the new additions to the touring squad.
Justin Basson (utility forward), Marnus van der Merwe (hooker) and Oupa Mohoje (looseforward) are all nursing knee injuries, while Dries Swanepoel (centre) and Anthony Volmink are out with ankle and calf injuries respectively, which has ruled them out of contention for selection.
The Toyota Cheetahs will depart for Ireland on Tuesday, 11 February, where they will kick off their tour against Conference A log leaders, Leinster in Dublin on Saturday, 15 February, before facing Ulster in Belfast and the Dragons in Newport.
Toyota Cheetahs touring squad:
Wilmar Arnoldi, Craig Barry, Clayton Blommetjies, Aranos Coetzee, Aidon Davis, Luan de Bruin, JP du Preez, Joseph Dweba, Louis Fouche, Benhard Janse van Rensburg, Sintu Manjezi, Charles Marais, Chris Massyn, Rabz Maxwane, Tian Meyer, Gerhard Olivier, Ruan Pienaar, Junior Pokomela, Tian Schoeman, William Small-Smith, Chris Smit, Rhyno Smith, Walt Steenkamp, Boan Venter, Reinach Venter, Jasper Wiese.