The Indian team for the tour would be selected in New Delhi on June 12 and the left arm seamer is unlikely to be picked for it.
BCCI sources said Zaheer suffered the injury during the second ODI of the Afro-Asia Cup series on Saturday.
He was taken to a hospital today by team physio John Gloster for a MRI which had revealed that he was suffering from a groin strain.
Refusing to disclose the contents of the MRI scan report, Gloster said, ''The Board will take a decision based on the report.'' The MRI report would be sent to the BCCI on Monday and the Board would take a final decision about Zaheer's availability for the forthcoming tour of Ireland.
The extent of the injury and whether he would be fit enough for the tour would be known only after the receipt of the MRI report, which was expected to be out tonight.
Zaheer bowled only 2.4 overs on Saturday and was rested for Sunday's match so that he did not aggravate his injury.
India would play three ODIs against South Africa in Ireland from June 26 ahead of the full tour against England next month.