The collision, which involved a blue Vauxhall Vectra and a grey VW Golf, occurred on the A171 at Normanby, just south of Whitby, at around 10am yesterday (Saturday).
Police said that early indications suggest the Vauxhall was travelling on the A171 towards Whitby when the car appears to have lost control and crossed the road into the path of on-coming vehicles.
The car then struck the VW, which caught fire when it came to rest on the grass verge, said police.
Traffic Sergeant John Lumbard, of the Roads Policing Group said: “The infant was being carried in a child seat in the Golf.
The mother, who was the driver, was seriously injured as a result of the collision.
"Due to the brave actions of members of the public, both mum and her child were rescued from the car before it was engulfed in flames. Thankfully the baby was uninjured.
“I sincerely thank all those who stopped at the scene to assist during this extremely dangerous situation. They showed immense courage and their quick actions almost certainly prevented a tragic outcome.”
The mother, who is aged 32 and from Whitby, was taken by ambulance to James Cook University Hospital in Middlesbrough with a serious leg injury. Her condition is described as “comfortable”.
An 18-year-old man from Scarborough, who was a passenger in the Vauxhall, suffered serious internal and arm injuries and was taken by air ambulance to the same hospital. His condition is described as “very poorly”.
The driver of the Vectra, a 36-year-old man from Scarborough, also received treatment at the hospital for a foot injury before being discharged. He is the stepfather of the 18-year-old man.
Police are keen to hear from any witnesses who may have seen the collision or recall seeing the two vehicles beforehand. They are particularly interested in speaking to the driver of a car which was travelling behind a HGV tanker and in front of the VW Golf travelling in the direction of Scarborough from Whitby.
Anyone with information is asked to call North Yorkshire Police on 101, select option two and ask for Huw Walkey or the Major Collision Investigation Team. Quote reference number 12170166359.