Nine-month-old Charlie was in his pram when two men launched a firework at the family before it went off next to them.
Charlie was rushed to hospital to find that it was his badly burnt snowsuit that had saved him from any injury.
Charlie's 19-year-old-mum, who only wanted to be named Chloe, suffered 24 burns in total and has been told that she will be "scarred for life".
She said: "My son was burnt, so the paramedics took his suit off to make sure it hadn't gone through. They were obviously very shocked because the suit had saved him.
"Doctors said it practically saved his life."
Chloe, who was pushing Charlie in his pram at the time of the attack in Hull, said she was out walking with her partner and their dog on Saturday night before it happened.
She said a firework was thrown towards them, then flew underneath Charlie's pram and exploded against the wall next to him.
Chloe said: "We saw some people playing around with fireworks outside the Bosun pub. We didn't know what was happening at first.
"We saw the men light a firework, but thought it was a Catherine wheel that they had left on the floor.
"Then all of a sudden it came shooting towards us and we didn't have time to move out the way - it just happened so fast."
Chloe says her dog anticipated the attack and dragged her partner, Brandon, 19, away before the firework hit him.
Charlie was asleep in his pram when the firework exploded and he woke up shrieking.
Chloe said: "My legs were burning and I ran into the road in tears, screaming. I was petrified because at that point I didn't know what had happened to my son.
"He was really scared because it banged right next to his pram. He screamed all the way to the hospital and I just couldn't calm him down."
Chloe has been left with burns on her face and chest and was been told three of the injuries will leave her scarred for life. Brandon also suffered minor burns.
But although the flames from the firework burnt Charlie's snowsuit, he was unhurt.
Chloe said Charlie had only just started to wear the suit as the weather got colder, and wearing it meant he had a very lucky escape.
She said: "I was going to put Charlie in some jeans and a T-shirt, but my partner said to put him in the snowsuit instead.
"I'm glad we changed his outfit because it could have been a lot worse. We'll definitely be investing in another suit."
After the attack, Brandon went across the road to confront the men, but they allegedly threatened him and told him they would burn the family's house down.
A spokeswoman for Humberside Police said: "Police are investigating reports of malicious wounding as two people were injured when a firework ignited next to them as they walked along Hessle Road in Hull.
"The man and woman sustained burns as a result of the incident.
"The couple's baby, who was being pushed in a push chair at the time of the incident, was not harmed."
Police described one suspect seen outside the Bosun pub as being tall, bald, aged about 30 and wearing a dark jacket.
The other was described as about 60 years old, tall and of skinny build with grey hair.
Enquiries are continuing and anyone with information should call Humberside Police on 101, quoting the crime reference number 2148578.