Mr Justice Hayden has ruled that doctors at Alder Hey Children's Hospital in Liverpool can stop treating Alfie against the wishes of his parents.
Hundreds of protesters gathered outside the hospital on Thursday, a day after judge Mr Justice Hayden endorsed a plan for Alder Hey doctors to withdraw life support treatment from the child.
Appeal court officials say a hearing has been listed for Monday.
Members of the public descended on the hospital last night after Alfie's dad Tom posted on his social media asking for a peaceful protest, after High Court judge Justice Hayward made a decision to turn off the 23-month-old's life support machine.
His parents, Tom Evans and Kate James, have lost legal cases over their son in the High Court, Court of Appeal, Supreme Court and European Court of Human Rights.
The lawyers representing Alfie's parents, the Christian Legal Centre, released a statement this afternoon saying that the toddler's life support can not be turned off until the appeal is heard on Monday, April 16.
Roger Kiska of the Christian Legal Centre, representing Alfie's family in court, said the family should be allowed to take Alfie overseas to try foreign treatment which has been offered to him.
The judge said detail of that plan could not be revealed because Alfie was entitled to privacy at the end of his life. Alfie will continue to receive treatment pending that hearing.
Footage posted online showed Alfie's parents receiving huge applause as they joined the significant crowd of protesters who were chanting Alfie's name.
Evans said the documentation proved he was allowed to leave legally, and that he had removed the duty of care and given it to their air ambulance company.
One document, a letter from the Christian Legal Centre, said that given the medical professionals, transport, and life support equipment the family had prepared, "such a removal would be lawful under English law".
"The alarm was pulled and police were alerted and within a matter of 15 or 20 minutes I had three police officers round the bedside telling me that Alfie was a ward of court and they had been notified by the hospital and if I touched my son I would be arrested for assault".
"I know the date and time my child is going to die and we haven't even had time as a family to come to terms with this", she added.
Following last night's protest, Mr Evans and his partner Kate James have issued a press release thanking those who came out for Alfie.
Alfie has been at Alder Hey since December 2016 with an undiagnosed degenerative brain disease.
Merseyside Police said on Thursday night that they were at the protest outside Alder Hey Children's Hospital and said access to the hospital was being disrupted.
Alder Hey said it experienced "significant disruption" due to the protest.