The fourth child was critically injured after the incident at Wyndham Vale, south west of Melbourne, on Wednesday.
The mother, 35, has been released from police guard in hospital and is talking to the Victorian Police homicide squad.
Police said they were still trying to understand what made the car run off the road.
They have been talking to local people about the background of the family - originally from Sudan - and their movements on Wednesday.
When emergency services arrived at the scene the woman and the four children, all believed to be aged under six, were in the car.
One child died at the scene, one died on the way to hospital and the third child died in hospital. The fourth child, a five-year-old girl, remains in a serious condition at Melbourne's Royal Children's Hospital.
Superintendent Stuart Bateson called on members of the local Sudanese community to help police with their investigations.
"We understand that there may be some social, cultural and religious implications impacting on the community but let me reassure you that we will remain respectful of those issues at all times," he said.
"We do need to understand what was happening in their lives and we do need to understand what their movements were leading up to the incident."
Local media have reported the mother and children were part of a family of seven children, who came to Australia from what is now South Sudan in 2008.
Melbourne police are questioning a mother who was driving a car carrying four of her children when it plunged into a lake, killing three of them.