He said the birth proceeded "uneventfully" and the baby was tested after delivery.
"The baby unfortunately also tested positive, but the good news is that both mother and child are well."
Bux said they both have been discharged and are recovering at home.
He said "all the necessary precautions" were taken in the maternity ward and in theatre.
"Necessary cleaning was done after the procedures."
Bux said expectant mothers could take comfort in the fact that they would be screened before being admitted. "Your status will be known to the doctors and hospital so you can be treated appropriately and won't pose a risk to other patients."
He said the hospital had three other patients in its high-care facility who had tested positive for Covid-19, and one was expected to be discharged soon.
Bux said the hospital had stringent measure in place, including a screening tent set up outside the hospital.