Speaking at the start of anti-bullying week, the minister said that schools would get the power to ask courts to order parents of bullying or badly-behaved pupils to attend parenting classes. If they failed to do so, they could face fines of pound;1,000.
Ms Smith said: "Bullying should never be tolerated in our schools, no matter what its motivation. Children must know what is right and what is wrong, and that there will be consequences for crossing the line.
"We will also be sending a strong message to parents that schools will not tolerate a failure to take responsibility for bullying behaviour."
Margaret Morrissey, of the National Confederation of Parent-Teacher Associations, said: "If you've got a 14-year-old boy, how are you going to police his actions 247? Realistically, you can't stop every single case of bullying. And, if a family can't cope financially, a fine will make things worse, rather than better."
Ms Smith said the Government's white paper would take up recommendations made last month by the behaviour taskforce led by Alan Steer, head of Seven Kings comprehensive, in east London.
This would give teachers a legal right to discipline pupils, and heads the power to search pupils for knives and other sharp weapons.
Ms Smith said that parents would be compelled to take responsibility for excluded pupils during the first five days of a suspension.
To coincide with anti-bullying week, Gordon Brown, the Chancellor, has launched a new programme which will train Girl Guides to combat bullying.
The "Beatbullying" initiative will encourage Guides to act as anti-bullying advocates in their schools, working as peer mentors and supporting bullying victims.
The second annual anti-bullying week has drawn the support of a number of celebrities.
Among them is Anthony Hutton, winner of the latest series of Big Brother.
The 23-year-old said that his teenage cousin has been bullied as a result of his appearance on the Channel 4 show.
"Bullying is a horrible, terrible thing," he said. "Some kids have an absolute nightmare at school, and can end up committing suicide. We need to make people aware of this."
Kenny Frederick, Opinion 23