The family of five were suffering from nausea and light-headedness at a home in Sydney’s southwest about 8am.
The mother and children, aged two to 13, were found upstairs in one of the bedrooms.
The generator had been running for about 45 minutes after the home’s power went out in the storms.
Marcus Hunziker, who works in special operations for NSW Ambulance, said it was a very scary call out.
“When carbon monoxide is involved there can be dire consequences,” he said.
“This could have been a lot worse today.”
He said the family were “very, very lucky”.
They were taken to Liverpool Hospital in a stable condition, where they received oxygen treatment.
Mr Hunziker said monoxide poisoning could be difficult to treat.
“There are significant dangers when it comes to these sort of jobs – where not only the patients, but emergency services can also become exposed,” he said in a statement to 7 News.
“While the symptoms can be similar to a cold – it has the potential to be deadly if exposure is left too long.
“Carbon monoxide starts to replace oxygen in the body, which we all need to function, when there is prolonged exposure, the symptoms can elevate and patients can have an increased shortness of breath, confusion, blurred vision, loss of consciousness and, in the worst case, even death.”