The HSE is urging parents to "cocoon" very young babies as 829 new cases of RSV have been identified over the past week.
It said that babies and children under four, the elderly, and vulnerable, have been most commonly affected as the amount of patients being admitted to hospitals due to flu had doubled last week.
RSV causes bronchiolitis, which is a common chest infection in babies and young children.
The virus spreads when someone coughs or sneezes and it mostly affects babies and young children under two years old, especially babies under six months old.
In a statement, the HSE said: "People are urged to help limit the spread by cocooning very young babies, practicing respiratory etiquette (covering coughs), and making sure all vaccines are up to date, including flu and Covid-19."
Up to 40 children a week have been admitted to intensive care as a result of RSV since the beginning of November.
Dr Abigail Collins, National Clinical Lead for the HSE's Child Health Public Health Programme, advised parents to look out for symptoms such as coughing, wheezing, a runny nose, difficulty feeding, a sore throat, or fevers.
She said: "The best advice comes back to respiratory etiquette, covering coughs and sneezes, alongside regular hand washing. All very important to limit the spread of respiratory illness.
"We advise people with babies, particularly very young babies, to try to cocoon them and avoid having them in large crowds, or near people with cold and respiratory symptoms.
"If your child is sick, keep them away from other children and vulnerable adults where possible."
Last week saw the highest weekly number of hospitalisations caused by RSV cases in Ireland, surpassing the peak of last year's surge.
People have been urged to help limit the spread by covering coughs and making sure all vaccines are up to date, including flu and Covid-19.
The HSE said it is managing 23 outbreaks of respiratory illnesses across its acute hospitals.
Dr Greg Martin, National Clinical Lead for Health Protection Surveillance, said that most cases of RSV and flu can be cared for at home, and usually clear between two and three weeks without treatment.
However, he said parents and caregivers need to be vigilant of symptoms and always contact their GPs if they are worried.
"Especially if symptoms get worse quickly," he said.
