Parents will face a legal duty to co-operate with plans to make education and training compulsory in England until the age of 18.
The government wants young people to remain in education
Youngsters who fail to comply can face spot fines or community service.
But the legislation outlined in the Queen's Speech indicates that parents will also have legal responsibilities.
The Education and Skills Bill says they will have a duty to "assist their children to participate" with the regulations, fully effective from 2015.
A Department for Children, Schools and Families spokesman said that parents who deliberately obstructed their children from staying in education could face parenting orders.
But he emphasised that parents would not face the type of fines imposed on parents of truants - and that the responsibility to attend would primarily rest with the young person.
The legislation will raise the leaving age to 17 in 2013 and then to 18 in 2015 for all pupils in England.
The Welsh Assembly will be empowered by the bill to do the same, but its government has indicated that it will not do so.
Teenagers who fail to comply face spot fines of £50 and fines in court of up to £200.
Young people will not necessarily be remaining in the classroom - as vocational training will be offered as an option.
By 2013, under separate legislation, school leavers will be entitled to an apprenticeship place - with plans for 400,000 apprenticeships in England by 2020.
But there have been questions raised about the sanctions which will be applied against teenagers or their parents who refuse to comply.
The National Union of Teachers general secretary, Steve Sinnott, backed the raising of the leaving age - warning that 16-year-old drop-outs faced "dead-end lives".
But he warned that "the government has to be very careful that any sanctions do not backfire and lead to the ghettoisation of those young people who will be the hardest to reach".
Margaret Morrissey from the National Confederation of Parent Teacher Associations questioned the practicality of fining feckless parents.
"Unfortunately, 99% of the youngsters who drop out are probably the ones whose parents will have tipped them out of the door. How are they going to get these parents to take responsibility?"
John Dunford, general secretary of the ASCL head teachers' union, said that an enforcement system was important.
Dr Dunford said it would "make sense to extend the truancy system used for schools to 17 and 18-year-olds".
But he warned that sanctions "should only be used as a last resort, not least because they could be difficult for providers to administer".