The bill allows minors to ask for euthanasia on the grounds that their illness is terminal, that they are in great pain and that there is no treatment to alleviate their distress.
The request has to be agreed by the patient's medical team and approved by the child's parents.
"We want this law to be passed before the dissolution of parliament," said Socialist MP Karine Lalieux.
Belgium introduced euthanasia in 2002 for those aged 18 and over, and would follow in the footsteps of neighbour the Netherlands which allows mercy killing for children over 12.
The Belgian legislation does not set an age limit but states that the patient has to be conscious of their situation and understand the meaning of a request for euthanasia.
It is thought that there would be only 10-15 cases a year, based on statements from doctors and nurses that the practice exists outside the law for terminally-ill youngsters in physical distress.
Last month, 16 paediatricians urged lawmakers to approve the legislation.
"Why deprive minors of this last possibility," they said in an open letter carried in the press, arguing that under-18s were able to make an informed and mature decision when facing death.
"Experience shows us that in cases of serious illness and imminent death, minors develop very quickly a great maturity, to the point where they are often better able to reflect and express themselves on life than healthy people."
A recent poll shows three quarters of Belgians approve the move but a group of Christian, Muslim and Jewish leaders oppose it as undermining the value of human life.
After the Netherlands and Belgium, Luxembourg in 2009 also approved euthanasia but for adults only. In Switzerland, doctors can assist a patient seeking to die but euthanasia itself is illegal.
Belgium logged a record 1,432 cases of euthanasia in 2012, up 25 percent.