The youngster was rushed to hospital critically injured on Thursday evening but died on Friday.
Civil Guard officers leading the hunt for the person who killed him released video grabs of the suspect vehicle - a red car thought to be a Volkswagen with black tyres - as they appealed for the public’s help.
They said in a tweet released hours before the youngster lost his fight for life: “Do you know who ran over a boy aged 10 and then fled the scene without helping him?
“The youngster is fighting for his life in intensive care in hospital.”
It's believed the hit-and-run happened around 8.30pm on Thursday in a street called Calle Dublin - Dublin Street in English - in Adeje in the south of the island.
The youngster, who died at a hospital in the capital Santa Cruz de Tenerife, was coming out of a shopping centre called the Gran Sur shopping centre with his family when he was hit.
He suffered head injuries as well as chest injuries which affected his right lung.
He was admitted to an intensive care unit at the University Hospital Nuestra Señora de La Candelaria from another hospital where he was initially taken after being stabilised at the scene.
He is understood to have died early yesterday evening/on Friday evening.
Civil Guard officers are being assisted by Spanish National Police as well as local town town-employed police in their hunt for the killer.
The youngster has not been named.
A spokesman for a regional government emergency response service confirmed immediately after the incident: "We received a call about a traffic accident involving a 10-year-old boy at 8.30pm on Thursday...Two ambulances went to the scene along with a doctor and nurse from a nearby health centre. One of the ambulances rushed him to Hospiten Sur with multiple serious injuries. He was subsequently transferred to another hospital."
Police say the hit-and-run car suffered frontal damage.
It is believed the driver fled the scene without getting out of his vehicle to see how the youngster was.
One local took to Twitter today/yesterday (SAT) to say he had already called police to give them the name of someone he suspected.
He said "I have seen that car on the road. There’s someone I suspect."
A police-run Facebook page said: “Colleagues in Adeje are still working on trying to track down the person responsible for the accident in which a boy from Ireland has died...National Police are helping in this task as well as Civil Guard and local police.
"The images are not great and several types of vehicles are being talked about including an Alfa Romeo.
The remains of glass at the scene are being investigated to see if the make can be pinned down...With the police working on the case and the public’s help, we’re going to be able to find this person."
In an earlier message, a spokesman said: “We are sorry to have to inform you that the boy run over in Adeje, an Irish national, has died.”