The girl, who has been named Roman by nurses, was found at around 10pm on Thursday in the park in Roman Road in East Ham.
Police said Roman was wrapped in a white towel and placed in the shopping bag on the ground next to a bench in the small children's play park.
The baby was rushed to hospital where she was in a stable condition on Friday morning, the Metropolitan Police said.
Roman was discovered by grandmother-of-one Rima Zvaliauskiene, 50, just 100 yards from her home while walking her dog, Scout.
Ms Zvaliauskiene, who used to be a midwife in her native Lithuania, told the Sun Online: "There was a crying noise from the bag. She was crying for her life. The baby saved herself.
"I removed the towels and when I saw the baby I realised it was newborn.
"I ran back to the house and brought back a blanket to put on the baby.
"I was worried but when I heard her crying I knew she was a fighter."
The woman called the emergency services while her son Ovidijus Zvaliauskas, 27, ran out from their family home to help her.
Mr Zvaliauskas told the BBC it was "terrible" adding that he had "no words" for the mother who abandoned the baby.
He added: "My mum was walking the dog and she heard a noise coming out from the bag.
"She rang me up because she was too scared to approach the bag."
Police said they are growing "increasingly concerned" for her mother's welfare as they believe she may be in need of urgent medical attention.
A photo issued by police showed the baby had been hooked up to an intravenous drip and monitoring equipment once she arrived at hospital.
Appealing directly to her mother, Inspector Shane Clarke, of the North East Command Unit, said: "I urge you to make contact either with police, your local hospital or GP surgery. It is really important that we know that you are safe.
"I would also urge anyone who has information that could help us to reunite this baby with her mother to come forward."