The video circulated widely by rights groups and local news media shows an armored vehicle used to launch tear gas veering sharply to partially run over and protester and then smash him into a police water-cannon vehicle.
The first vehicle then wheels around and drives off through a scattering crowd of demonstrators as some rush to aid the fallen man, who was in serious but stable condition Saturday, the Las Condes clinic reported.
Jose Miguel Vivanco, Americas director for Human Rights Watch, tweeted that the police acted "with extreme brutality" and said the officers and commanders involved in the incident should be fired and prosecuted.
The head of the National Human Rights Institute, Sergio Micco, visited the injured youth in the hospital.
Officials, too, expressed dismay.
"Images such as those of the youth hit in Plaza Italia don't leave anyone indifferent," said the governor of the metropolitan region, Felipe Guevara, in a tweet. "As a government and above all as governor, I profoundly lament what occurred and I send strength to him and to his family."
He said the incident and its context would be investigated.
Chile has been roiled by continuing and sometimes violent street protests since Oct. 18, when a student protest over a modest increase in subway fares turned into a much larger and broader movement with a long list of demands that largely focus on inequality.
A U.N. human rights report released this month accused Chilean security forces of serious human rights violations, including deaths, torture, sexual abuse and the use of excessive force.
Prosecutors are investigating more than two dozen deaths attributed to incidents during the protests.
Friday's incident involving the protester occurred in the historic Plaza Italia, which has been a focus for many of the demonstrations.
Police reported that they have launched 856 internal investigations, and they have fired eight riot police accused of "serious breach of protocols." Most cases are ongoing, more are ready for judgement and other officers have been acquitted, officials said this month.