Under British law, the National Health Service and local authorities can take legal action against parents who oppose treatments doctors say are necessary to save a child's life.
Justice Mary Hogg said Neon had recently undergone surgery for a brain tumour and needed urgent radiotherapy.
"His mother, Mrs Sally Roberts, who is also known as Sally Lees, is opposed to the treatment and has disappeared with Neon. "The doctors say that unless treatment is started next week, the prospects of Neon's surviving are dramatically reduced."
Justice Hogg had urged Mrs Roberts to attend the next hearing, set down for Friday (UK time), saying she was "deeply concerned for the welfare and wellbeing of this little boy".
Mr Roberts told the Daily Mail his wife was opposed to radiotherapy because it might damage Neon's "intelligence, growth and hormones".
"She wants to do everything she can and rely on natural remedies and things that are not too invasive, rather than radiotherapy and chemotherapy. She is worried about the damage that can be done. She wants him to be able to live a normal life."
Mr Roberts was also concerned about the side-effects but said the evidence was that Neon needed the treatment.
The Daily Mail said Mrs Roberts was "well-known in music circles" as DJ Sally. She has performed at London nightclubs and the popular Glastonbury Festival.