A Welsh Ambulance spokeswoman said the man and baby were taken from the Prestatyn fire to Glan Clwyd Hospital.
The man was later transferred to Whiston Hospital, Merseyside. The baby was transferred to Alder Hey Children's Hospital in Liverpool.
Both were said to be in a serious condition.She described the property as a house that had been converted into flats.
A special memorial service has been held in Prestatyn to celebrate the lives of five people who were killed in a house fire last month.
Funerals will be held for the five people who died as a result of a flat fire in Prestatyn last month.
Two people arrested following a fire in Prestatyn in which four died have been released from police custody.