The results of the test will be known later today.
No further information was given about the children being tested.
The spokeswoman said trained specialists were caring for them.
"Specialist medical staff are caring for the patients, using the procedures and equipment in which they have been trained," the hospital spokeswoman said in a statement.
"The safety of staff and the community is paramount."
A Victorian Health Department spokesman told the Sydney Morning Herald the children had flown in to Melbourne from overseas today.
The country of origin was unknown.
The children were taken to hospital for testing after the "standard screening processes" at Melbourne airport found the children had high temperatures, the spokesman said.
In a later statement, the Victorian Health Department said the initial clinical assessment suggested it was exceedingly unlikely the children had the virus.
The department also said the broader community was not at risk of contracting Ebola - regardless of whether a patient had the virus.
"While Ebola is a very serious disease, it is not highly contagious as it cannot be caught through coughing or sneezing," the department's statement said.
"The risk of infection is extremely low unless there has been direct exposure to the bodily fluids of an infected person or animal (alive or dead)."
The Royal Children's Hospital is designated to provide care for children under 16 for assessment and management of patients suspected of a viral haemorrhagic fever such as Ebola.
Ebola has claimed more than 8600 lives in West Africa since the latest outbreak began last year.
There have been no confirmed cases in New Zealand or Australia so far.
- AAP, nzherald.co.nz
