Police said the two children were found dead at the Longmuir Road address in Watsonia and a man was arrested at the scene just after 2.30pm.
He is now being interviewed by police.
Police are investigating the circumstances of the deaths, but it is believed they are known to each other.
Homicide Squad detectives are on the way to the scene.
An Ambulance Victoria spokesman said paramedics were called to treat two patients in a critical condition just before 3pm.
The patients were worked on by paramedics for some time at the scene, but could not be saved, the spokesman said.
MORE TO COME