"These disturbing allegations of enforced disappearance and death in custody, and possibly unlawful killing by police, must be immediately and fully investigated by an independent body," Malcolm Smart, the London-based group's Middle East director, said in the statement.
News of Shabaan's death emerged after a video of his funeral with interviews of family members and his lawyer circulated on social networking sites.
State-owned EGYNews.net website said Shabaan and a friend, Ahmed Farag, had stolen a cell phone from a woman and that passersby were able to tackle Farag, but that Shabaan escaped.
"While the investigation was being conducted, Sidi Gaber station received a report that the corpse of a drowned man had appeared in the Mahmudiya canal, and it was determined the body was that of Ahmed Shabaan," the news site reported.
A lawyer hired by the family, Ahmed Qutb Hamid, said Shabaan and Farag were returning from a friend's wedding on an unlicensed motorbike when police stopped them at checkpoint.
"They had a dispute with the police and were taken to the Sidi Gaber station," he said.
The family heard he was detained after his friends made inquiries at the station, but police refused to confirm they were holding him when family members tried to visit him.
"His body was found days later, when it rose to the canal's surface," said Hamid.
Shabaan's uncle, Ashraf Shabaan, told AFP he had seen the youth's corpse in the morgue and was convinced he had been tortured to death.
"He had cuts on his arms and bruises all over his body. His teeth were missing, and the fingernails on three of his fingers were gone," he said.
The body had already undergone an autopsy, he added.
The government says it does not condone torture, and that reported cases are isolated and offending policemen are punished.
Rights groups say torture is routine in the country.
Amnesty called on the government to ensure that Shabaan's friend, Farag, would not be abused.
The incident is alleged to have taken place in the same district where 28-year-old Khaled Said was dragged out of a cafe by two plain clothes policemen and severely beaten in June.
He died in their custody. Police say he choked on a bag of drugs concealed in his mouth but charged two policemen with using excessive force against him. They are standing trial.
Said's death led to several demonstrations in Alexandria and Cairo after pictures of his badly mangled face spread around the internet.
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