The incident, in Myatt’s Field Park, Lambeth, occurred at around 8.30pm on Monday, 19 July.
The toddler was in the park with her family when the collision happened, and she was taken to a south London hospital by her relatives.
Police were notified in the early hours of Tuesday morning after her condition deteriorated. She is in a stable condition but her injuries have been assessed as life-changing. Her next of kin are being supported by specialist officers.
Officers have reason to believe that the rider of the e-scooter, described as a young male who was with a group of people including another e-scooter and a bicycle, stopped after the incident to say sorry.
Officers from the Serious Collision Investigation Unit (SCIU) are investigating and conducting CCTV enquiries.
Detective Inspector Lucie Card, of the Met’s Roads and Transport Policing Command, said: “A little girl has been left in a serious condition after this collision and her family are, of course, very distressed.
“We have reason to believe that the e-scooter’s rider stopped after the collision and apologised to the little girl’s mother. It may be that they haven’t realised the severity of the girl’s injuries and thought she was ok.
“I am asking this person to please come forward and speak to us because we do need to understand what happened. I know it might feel a little overwhelming, but please do the right thing and call us or go to your nearest police station.
“We are also keen to hear from anyone in Myatt’s Field Park around 20:30hrs last night. Please do get in touch with us if you witnessed what happened, or have information about the circumstances.”
Any witnesses yet to speak with police are asked to call the SCIU at Catford Traffic Garage on 020 82851574 quoting CAD 7891/19JUL