Urrvashi Singh claimed midwives from Trafford General Hospital did not carry out thorough checks, which led to son Dilraj developing further illness.
Hospital bosses settled proceedings but have not admitted liability.
The court heard the trust was working with the family's legal team on the payout to cover Dilraj's care costs.
Seven-year-old Dilraj developed a jaundice-related brain disease called Kernicterus and has been left blind, unable to speak and with cerebral palsy.
Ms Singh said that during two home visits she told midwives "something wasn't right" but they did not check her son for jaundice.
When Dilraj lost weight and returned to hospital he was diagnosed and Ms Singh was told he had an hour to live.
Eddie Jones, a specialist brain injury lawyer at JMW Solicitors, said: "The real pity of this case is that the brain damage sustained by Dilraj was entirely preventable if he had been given the right treatment at the right time.
"Jaundice is a common condition in newborns and, whilst in rare cases the consequences can be serious, it is treatable. Sadly, the mistakes made have had a catastrophic impact on Dilraj's life and the lives of the rest of his family."
This case is one of a number of similar claims across the country, he added.
Ms Singh, 37 and from Stretford, said she had to give up her job as a nursery nurse to care for her son and has called for a national screening programme to identify cases.
She said: "More needs to be done to ensure that midwives are alert to the signs that babies such as Dilraj are in danger of contracting Kernicterus.
"There were opportunities missed to help my son. If only the link between jaundice and the risk of brain damage had been made early enough, something could have been done."
In 2006, the government's former Chief Medical Officer Sir Liam Donaldson, called for a national Kernicterus register and routine screening to prevent the condition occurring.
A spokeswoman for the Department of Health said there is currently no such register as it is a very rare condition.
"We screen for rhesus disease which is the main cause of severe neonatal jaundice which can lead to Kernicterus. This is led by midwives," she said.
"All midwives should be fully aware of the signs of neonatal jaundice and what to do about it."
A spokesman for Central Manchester University Hospitals NHS Foundation Trust said: "Following detailed investigations into the circumstances surrounding Dilraj's treatment, a compromise was reached in respect of liability.
"We are satisfied that a settlement has been reached and we wish Dilraj and his family well for the future."

Fly swarms from the Shows Waste Management site in Slack Lane, Derby, have left residents facing difficulties cooking and cleaning for weeks.
The Environment Agency said 2,200 tonnes of waste has now been moved and "the fly issue...has been resolved".
The site has been ordered by the agency to move all waste by 7 July.
The agency had started a criminal probe into the fly infestation, and a spokesman added they would "seek to take the appropriate level of enforcement action against relevant parties" once their investigation into the cause of the plague is over.
"We can confirm that the fly issue on the site has been resolved with no reported issues from the community since early June," an agency spokesman said.
"We will continue to monitor and assess the situation until our requirements have been fully met."
About 3,000 households and businesses are in the affected areas.
One resident, Melissa Marriott, previously told the BBC she has been unable to have a bath without flies getting into the water, and had to resort to buying an electric fly killer which "gets 50 flies a day".
Another resident, Jenny Warren, said the flies had been "all over the food and you can't open windows".
On 17 May, Shows Waste Management was given a suspension order by the agency and told no further waste would be accepted on site.
The waste company has said it was in the current situation because of a dispute with another firm.
A mother whose son was left brain damaged after midwives allegedly failed to act on signs of jaundice has won compensation at the High Court.
[NEXT_CONCEPT]
Residents whose homes have been filled with hundreds of flies from a Derbyshire recycling site have been told their misery is over.