Rizwan and Irfan both suffered hamstring injuries in the third match in Rawalpindi, where a second-string New Zealand side won by seven wickets to level the five-match series 1-1
His wife Ayesha Siddiqa Iqbal gave birth to a boy at a hospital in Thailand early Sunday.
"Our little bundle of joy has arrived! By the Grace of Almighty, we’ve been blessed with a baby boy early today," Tamim Iqbal wrote on his Facebook page at 12:15pm.
The Tigers' opener flew to Bangkok on Feb 20 after playing in Pakistan Super League in Dubai. He had already sent his wife there for the delivery.
Tamim has opted out of the ongoing Asia Cup to stay by his wife during the birth of their first child.