Scotland Yard said it was "very concerned" about the child, who was reported missing at 11am on Saturday after her distraught mother turned up at Guy's Hospital in London Bridge. A helicopter and sniffer dog search on Saturday failed to find the baby, who was last seen by staff at the hospital on Friday morning after receiving treatment for a skin complaint.
It is understood the mother went shopping with the baby and her six- year-old son in nearby Tower Bridge Road some time on Friday. The baby has not been seen since.
A Scotland Yard spokesman said: "We are very, very concerned for the safety of this child, whose last confirmed sighting was very early on Friday when her mother was seen leaving the hospital.
"A call was received from the hospital reporting the baby missing on Saturday morning and a full air and land search was carried out. That search continues. Obviously as time goes on we become increasingly concerned and we would appeal to anyone who might have seen the baby and her mother on Tower Bridge Road to contact us urgently."
The mother left Guy's wearing a long blue raincoat at around 5am on Friday and is believed by officers to have been seen on nearby Tower Bridge Road later that day.
A 35-year-old woman was last night being held in custody at a south London police station after being arrested in connection with the disappearance.
Anyone with information about the baby, who was last seen wearing a pink hooded jacket and blue romper suit, should contact Detective Inspector Graham Worthington at Deptford CID on 0181-853 1212.