Passengers called the police after finding the child - believed to be under two - in a buggy.
Now Haringey Council in North London has launched an inquiry.
The £377-a-week carer was with the child on the bus last Friday afternoon, believed to be heading to hospital.
But she got off the 491 on her own, leaving the infant on the single-decker in Enfield. Scotland Yard was alerted and the baby was then handed back to Haringey Council.
A spokeswoman for Haringey Council said: "The child was found safe and well and we are undertaking a full investigation.
"As soon as this incident came to light, steps were immediately taken to arrange a new fostering placement for the child."
A Scotland Yard spokesman said: "A woman, who identified herself as the child's foster carer, contacted emergency services.
"The child was checked at hospital before being handed back to the care of social services.
"Inquiries are ongoing. There have been no arrests. Social services are investigating the matter in partnership with the MPS Child Abuse Investigation Command."
Baby Peter was 17 months old when he died in Tottenham, north London, on August 3, 2007.
He suffered more than 50 injuries despite being on the at-risk register of Haringey Council and receiving 60 visits from social workers, police and health professionals over the final eight months of his life.
A series of reviews have identified missed opportunities when officials could have saved him if they had acted properly on the warning signs.
How could you leave a child that age on a bus? Beggars belief!