Nairobi governor Evans Kidero has set up an investigations team to look into at Mama Lucy Kibaki Hospital on Wedesday.
Eleven-week-old Dominic Otieno died at the hospital on Wednesday after waiting five hours for an ambulance to take him to Kenyatta National Hospital for specialised treatment.
County secretary Robert Ayisi said the hospital has four ambulances but three are broken down.
"It is very unfortunate to learn that a child’s life was lost. We have launched investigations and audit to ascertain the cause of death," Kidero said in a statement on Saturday.
"If indeed it was negligence by hospital personnel, then the responsible officer(s) will face prosecution. We are here to provide services to Nairobi residents and not to frustrate them."
The governor said staffing of doctors and nurses at the hospital is at an advanced stage to ensure efficiency and professionalism.
Money has also been set aside for completion of ongoing construction within the facility, as well as to improve the overall quality of healthcare.
"For a start, Sh8 billion, representing 27 per cent of our annual budget of Sh31 billion, has been allocated to the health sector," Kidero said.
"This is geared towards laying a strong foundation to ensure that Nairobi residents have a wide choice in as far as health facilities are concerned. Our health facilities treat about 8.5 million Nairobians annually.”