Bakhtawar Bhutto Zardari took to Twitter on Wednesday to thank everyone who wished her on the birth of her baby boy on Monday.
The baby was born a month early and is currently placed in the neonatal intensive care unit at a hospital in Dubai, where he was born.
She and her husband Mahmood Choudhry have not announced the baby's name yet.
The couple were married earlier this year and moved to the UAE where he is based.
This is the first grandchild for former president Asif Zardari and his late wife Benazir Bhutto.
Her siblings took to Twitter to share their delight at becoming an aunt and uncle.