A spokesman at the National Court in Madrid said the judge ruled Monday the couple must be held while the court considers whether to grant Britain an extradition request.
The judge could have opted to let the parents to go free while the case is considered.
The spokesman said Ashya King's parents told the judge they don't want to return to the UK. They were arrested yesterday in southeastern Spain after a European arrest warrant was issued by Interpol at the request of British police.
The spokesman said the legal process also involves requesting the advice of Spanish doctors and translating legal documents deemed pertinent to the case.