Ireland secured their first ever win over the Springboks in South Africa on June 11 with a 26-20 victory at Newlands.
Ireland coach Joe Schmidt said he was unlikely to bring in a replacement as he has options within the squad to deal with the loss of the 23-year-old.
"There are guys on standby so we can go back to them," Schmidt told Irish media. "To be honest, if we can cover it internally we probably will at this stage.
"It's pretty difficult to get them up to speed and to get them down here is a bit of a mission even."
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Henshaw was previously sidelined for six weeks after fracturing his left hand in Connacht's derby victory over Munster late last year.
(Reporting by Ian Rodricks in Bengaluru; Editing by Peter Rutherford)
