The Royal Children's Hospital says it is under pressure because parents are needlessly overlooking other hospitals.
The hospital says it has seen a 15 per cent increase in admissions to its emergency department, most of which are not critically ill.
The increase coincides with its relocation a year ago.
The hospital's chief executive, Christine Kilpatrick, says parents should take their children to their local hospital.
"If their child needs care, the message is go to a hospital as close to their home as possible."
"If they do require care in a tertiary facility such as Monash or the Royal Children's then they'll be sent on and transferred appropriately," she said.
The opposition's health spokesman, Gavin Jennings, has blamed a lack of government investment in the state's hospitals for the problem.
"Today it's the Royal Children's Hospital emergency department, but it could be their elective surgery waiting lists, or it could be at the Monash Children's redevelopment that hasn't started," he said.
Mr Jennings says the issues aren't limited to the state's major hospitals.
"Other hospitals right across Victoria are doing it hard because of under-investment by the Baillieu Government," he said.