All-rounder Afridi was due to meet up with the Irish team after completing his commitments with Pakistan against India in the two-match tournament in Abu Dhabi this week.
But the Irish Cricket Union (ICU) said Friday that the player, one of two overseas players in the squad, had to alter his plans.
"We have been alerted to the fact, that due to an illness with a family member, Shahid Afridi has been forced to make an urgent trip to Pakistan," said an ICU spokesman.
"He will not be arriving in Ireland as scheduled on Friday, but we are hopeful that he will be here on Saturday, in time for our C&G clash with Hampshire at Clontarf."
A spokesperson for Afridi said: "In conjunction with the ICU, our first thoughts are with Shahid and a speedy recovery for his daughter. All parties concerned are hastily working to ensure Shahid arrives in time for the opener at the weekend once other matters are resolved."