A picture posted on Facebook showed Ashya with his mother Naghemeh King
The health of a five-year-old boy taken from hospital by his parents against medical advice will deteriorate rapidly as the battery on his feeding system runs out later, police said.
Ashya King, who has a brain tumour, was taken from Southampton General Hospital and is believed to be in France.
He was allowed to leave the ward under the supervision of his parents.
It has also been confirmed the family are Jehovah's Witnesses, but there is no suggestion this is why he was taken.
Brett King, 51, and Naghemeh King, 45, removed him from the ward on Thursday.
A spokesman for the hospital, which contacted police six hours after they left, said: "Ashya was a long-term patient who was permitted to leave the ward under the supervision of his parents as part of his ongoing rehabilitation.
Ashya's father was pictured taking him from the
"When the length of time he had been absent became a cause of concern to staff yesterday afternoon they contacted police after a search of the site and attempts to contact the family were unsuccessful."
Interpol has a missing persons alert out for Ashya to all 190 of its member countries.
The organisation said it was asked to issue the "yellow notice", usually circulated to locate minors, by the UK authorities.
It was "treating all incoming information relating to the case as high priority", it added.
Speaking at a news conference, Assistant Chief Constable Chris Shead of Hampshire Constabulary said "time was running out" for Ashya.
"It is vital that we find Ashya today, his health will deteriorate," he said.
Mr Shead said Ashya was in a wheelchair and needed to be fed through a tube which is battery operated and the battery will run out today.
"If he doesn't receive urgent medical care, or the wrong treatment is given, his condition will become life-threatening.
"If Naghemeh or Brett or any of their children see or hear this appeal please take Ashya to the nearest hospital."
Mr Shead said they were told by the hospital the youngster was missing at 20:35 BST on Thursday - more than six hours after he had been taken by his parents.
On why it took six hours for the hospital to alert police, he said: "That is something that we need to look at."
Officers were keeping an "open mind" on the motives behind Ashya being taken, Mr Shead said.
The Office of Public Information for Jehovah's Witnesses said in a statement: "There is absolutely no indication, as far as we are aware, that their decision is in any way motivated by any religious convictions."
"Jehovah's Witnesses are encouraged to seek the best medical treatment for themselves and their children," it added.
It is believed Ashya's parents and six siblings boarded a cross-Channel ferry from Portsmouth to Cherbourg at 16:00 BST and arrived at 20:00.
Police said Ashya, who recently had surgery, cannot communicate verbally and is immobile. He is likely to be in a wheelchair or buggy.
Becky Kelly, BBC News
According to Ian Pople, consultant neurosurgeon at Bristol Children's Hospital, the battery in the feeding machine used by Ashya can't be changed easily.
It is integrated with the machine, much like an iPhone, and it means the machine has to be taken apart to replace the battery.
It's also not designed to be run on batteries for a long period and is usually plugged into mains.
In other words it's only battery reliant for short periods, such as going to the toilet, or moving between wards.
Cherbourg Police has confirmed it is searching locally for Ashya, checking hotels and CCTV.
But vice-prosecutor Cyril Fournier said he arrived late on the investigation and was only told Ashya was missing at 10:00 BST.
He said "they may have stayed in Cherbourg, but they may be 500km from here, it's like looking for a needle in a haystack".
An image of Ashya being wheeled out of the hospital by his father has been released by police.
The force said it was working with police in France to activate emergency child rescue alert procedures.
The family, from Southsea, Portsmouth, were travelling in a grey coloured Hyundai I800 Style CRDI, registration KP60 HWK.
Naveed King spoke about his brother's illness in a video posted on YouTube
Det Supt Dick Pearson, of Hampshire Constabulary, said: "If we do not locate Ashya today there are serious concerns for his life.
"He is receiving constant medical care within the UK due to recent surgery and ongoing medical issues. Without this specialist 24 hour care, Ashya is at risk of additional health complications which place him at substantial risk.
"He needs to be taken to a medical facility for his urgent health requirements as soon as he is located."
Clive Coleman, BBC legal correspondent
Parents have the right to remove their children from hospital unless they are prevented from doing so by a court order - it has not been confirmed whether Ashya was subject to an order.
If doctors are concerned that parents intend to remove a child, deny it the medical treatment it needs, and expose it to the risk of serious harm, they can seek a court order.
This will normally involve CAFCASS (the Children and Family Court Advisory and Support Service), the non-departmental public body which provides guardians to represent the best interests of children in family court proceedings.
Once an order is in place, any parent who removes their child in breach of the order is committing a contempt of court for which they could be imprisoned.
Police have launched a social media appeal and are urging people to share it, particularly with friends or relatives in France and bordering countries.
Ashya's paternal grandmother, Patricia King, said his parents were "wonderful" and had been left beside themselves at their child's plight.
Speaking from her home in Southsea, she said of her son: "He's the most caring and wonderful father you could ever have. The kids love him."
She praised her daughter-in-law, saying she had kept a bedside vigil while Ashya was in hospital.
She said she did not know whether Ashya's illness was terminal, saying: "I knew he was seriously ill, we all knew that."
Ashya's brother Naveed King posted a YouTube video on 23 July speaking about the five-year-old's illness.
Police are looking for Ashya's parents Brett King and Naghemeh King
It is believed Ashya is still in France with his parents and six siblings
The family were travelling in a grey coloured Hyundai I800 Style CRDI, registration KP60 HWK
He said: "I haven't slept anything really, I've been awake all night worrying.
"Everyone is sending their love now. We love you so much and we want to see you very soon and I love you so much and can't wait to see you.
"No kid at the age of five deserves to have a brain tumour."