Violence erupted on Thursday after residents blockaded the compound of the oil exploration company Emerald Energy.
They were demanding its help to repair and build new roads in the area.
A civilian was also killed and nine oilfield workers captured alongside the police officers. Video showed the hostages sitting in a crowded room on rows of chairs and on the floor.
Colombian President Gustavo Petro said he hoped they would be “unilaterally” released before any escalation of violence, and asked for medical help from the Red Cross.
Many of the protesters are rural and indigenous people who want Emerald Energy to build new road infrastructure around the San Vicente del Caguan area.
The oil company did not respond when approached by Reuters news agency for comment.
Colombian police paid tribute on Twitter to the police officer killed in the clash, who they named as Ricardo Monroy.
“Today we are more united than ever,” they wrote, adding that Mr Monroy had “offered his life in the line of duty”.
Local government officials said the officer died from a machete attack, while the civilian was killed by gunfire.
Colombia’s human rights ombudsman Carlos Camargo – who was on site to mediate – said he had spoken to protesters and stopped them from throwing petrol bombs at the oil facility.
Protests in areas near energy and mining operations in Colombia are common as communities demand companies build infrastructure, including roads and schools.
Police said a dissident subgroup of Farc rebels which rejected the 2016 peace deal were present in the region and may have been provoking the unrest.
Separately, Mr Petro on Thursday unexpectedly published a statement on Twitter asking the country’s prosecutor general to conduct a criminal investigation into allegations of corruption involving his own son and brother.
The statement did not specify the accusations against his eldest son, Nicolas Petro Burgos, and brother, Juan Fernando Petro Urrego, but it did say: “my government will not give out benefits to criminals in exchange for bribes”.