The court heard police were awaiting more information from medical staff at Auckland Hospital on the baby's condition.
A spokeswoman for St John said staff assessed, treated and transported one patient with "critical injuries" to Auckland City Hospital.
Innes, whose occupation is listed in court documents as a prostitute, is not to have any contact with the mother of the baby and is set to reappear in court on September 15.
Both police and St John were called to the property in Swanson around 7.54am on Sunday.
Neither Starship children's hospital nor police were able to provide an update on the baby's condition tonight.
On Sunday afternoon, police confirmed that an investigation was underway after "a person was located with serious injuries" at the Swanson address.
"Police are working to establish the circumstances that led to the injuries and at this stage there is no further information available."
Two armed officers, a dog handler, a forensic photographer along with detectives were at the scene as a full scene examination was carried out.