The thirtieth and last of the sessions will take place on October 24, said Jana Kulhankova, spokeswoman of the Proton Therapy Centre of Prague.
"Ashya left the intensive care unit on Tuesday and has been put in an individual room," she said.
He has "started to put on weight, he is smiling, and he is reacting to the gestures of his parents and those close to him," he said.
King's case made headlines after his parents removed him from a hospital in Britain in August against doctors' wishes, sparking an international manhunt.
He began treatment in Prague in mid-September, where he is put under general anaesthetic for the therapy, which is not available in Britain.
It is touted as more precise than conventional radiotherapy as it uses a proton beam to target only malignant cells in a highly precise manner.
Ashya arrived in Prague on September 8 from Spain where his parents had taken him after whisking him away from Southamption General Hospital in England because they feared that traditional radiotherapy would damage his brain.
His parents were detained in Spain on an international warrant, after British authorities suspected they were not acting in the best interests of the child.
But after the couple spent four days in a Spanish prison, a British court reunited them with their son in a Spanish hospital and allowed them to travel to Prague for the treatment.