The human rights group accused the department of a high number of police abuses, including torture and extrajudicial killings. The group also accused police of throwing tear gas while people tried to help the victim, 22-year-old Willy Florian, after he was shot Thursday.
"Florian's tragic death should lead to urgent measures to prevent more unlawful killings in the future," said Javier Zuniga, special adviser to Amnesty International.
Florian was shot as dozens of students protesting a sales tax increase clashed with police, but he was not one of the demonstrators. A police officer and a bus ticket collector who also was not participating in the protest were injured.
Authorities said they had a video of one protester firing a weapon at police.
The department has appointed a commission to investigate the shooting.
Police chief Jose Armando Polanco on Friday blamed the police commander in charge at the protest. He "did not do what was needed to ensure that these police officers store their weapons and not use them," the chief said.
At least 19 officers were detained after the shooting at the Autonomous University of Santo Domingo, the Caribbean country's largest university.
Dominican President Danilo Medina has called for an investigation and condemned the use of violence.
Medina presented the disputed tax legislation as a way to help close the $4.6 billion deficit in the government's budget. The measure was approved and will increase the general sales tax to 18 percent from 16 percent. It also will raise the price of gasoline 5 cents a gallon and impose taxes on basic food products, including a 10 percent tax on coffee and cooking oil, a levy that is increase to 18 percent by 2016.