Tamir Rice was shown on CCTV waving a pellet gun outside a recreation centre last November, before being shot twice. He later died in hospital.
Judge Ron Adrine said there were sufficient grounds to prosecute Officer Timothy Loehmann with murder, manslaughter and reckless homicide.
It will now be up to prosecutors to decide whether there will be charges.
Community leaders and activists this week had taken the unusual step of requesting the court to look at the case.
The judge also said another police officer, Frank Garmback, should face criminal charges.
Police have maintained that Rice's pellet gun looked real and that they asked him to raise his hands three times.
But his family said video footage shows the police acted too quickly after arriving at the scene.
Recordings of radio communications reveal a police officer at the scene describing Tamir Rice as aged "maybe 20" after the shooting.
Rice's death sparked protests in Cleveland, at a time when the deaths of black men at the hands of police had sparked a national debate.
A policeman who shot and killed a 12-year-old boy in Cleveland, Ohio, should be charged with murder, says a judge.