The fines are proposed in a draft Bill that is intended to make parents take more responsibility for their children's education. The Bill also suggests setting up school attendance panels to look at absenteeism.
Parents would face a fine of $1,000 the first time a child truanted, and $2,500 on each subsequent occasion. Pupils caught truanting could also be fined up to $100.
Parent organisations were outraged by the proposal and said they would oppose it. However, the Western Australia Teachers Union spokeswoman said teachers believed in compulsory education and that under the law, pupils were required to go to school.
"The fact that there is such a requirement means there should be some penalty for non-attendance," she said. "However, we would prefer that some form of conflict resolution procedures be in place before parents are taken to court. The problem is that the parents most likely to be involved are those who could least afford to pay such a fine."
A parent spokeswoman said there were often deep-seated reasons why pupils showed little interest in school and parents probably did not know that their children were not attending.
"There must be some positive ways of encouraging children to attend school, " she said.
The government has released the proposal for public consultation and will put the Bill before state parliament later this year.
The federal government will also try to compel parents to assume greater financial responsibility until their children are 21.
Under a new, single youth allowance system announced last week, study benefits or other welfare payments available to young people will depend on their parents' combined incomes, even if they no longer live at home.
Unemployment benefits for under-18s will be abolished next year to force thousands back into school.
The decisions were widely condemned by educators, parent groups and youth workers who said they were the harshest imposed by any federal government in years. Critics warned that suicides among young people would rise and that schools would face increased problems of motivation, discipline, overcrowding and under-funding.
At least 35,000 unemployed 16 and 17-year-olds will be prohibited from claiming the dole while an equal number will have their welfare or study benefits reduced. The government said the intention of the changes was to encourage teenagers to continue studying.
But teachers are against a large group of unmotivated students flooding back into the classroom. They say schools will have to expand vocational education and training courses and reduce the emphasis on academic learning.
One teachers' union official said: "No matter how hard you try to convince them that staying on at school enhances their skills to help them get jobs, they know they are at the bottom of the pecking order and they know they are not likely to get a job."
MPs say that removing the financial incentive for young people to leave school, forcing them to stay on or find a training place, is more acceptable than providing taxpayer-funded support for those without job prospects.