A third person was in critical condition and had been taken to a local hospital, Roger Larico, the mayor of the district of San Gaban in the region of Puno added by phone.
Peru has been a leading producer of cocaine for decades, despite efforts by consecutive governments to capture drug traffickers and stop farmers from growing coca.
The unrest comes a day before U.S. Secretary of State Mike Pompeo visits the Andean country as part of a four-country tour of South America to discuss Venezuela and regional relations.
Images on local TV showed people running as police fired tear gas on a road in the countryside.
Larico said the clashes started after authorities arrived unexpectedly to San Gaban to uproot coca plants before dawn. Witnesses told Larico that police shot live bullets recklessly during the clashes, he said.
"They were shooting right and left. That's why we have this bloodshed," Larico said.
A spokesman for the police confirmed that two people had been killed in the clashes but declined further comment until the government publishes a statement later on Friday.
Coca growing in Peru has been expanding in recent years, and the White House estimated late last year that Peru's potential cocaine production rose 20 percent to a 25-year high of 491 tonnes in 2017.