"We are stunned and heartbroken by this senseless tragedy," Steven Cook, the top administrative official of the local school district, said in a statement.
"No words can adequately express the grief our community is experiencing."
Emergency services responded to reports of an active shooter at Silver Rail Elementary in Bend, Oregon, at 12:59 local time (04:59 BST), Bend Police Department spokeswoman Sheila Miller told reporters.
The first call came from a person who said that an unknown suspect was shooting into their car with a long gun, police say. Photos released from the scene show a red truck with bullet holes.
Minutes later, the local county dispatch received multiple 911 calls reporting that the attacker had entered the school.
Police say he shot at locks on the doors in order to force his way inside.
A bystander saw the shooting begin to unfold, pursued the attacker into the school and shot him dead, police said.
Three minutes later, officers arrived at the scene. They confirmed that the attacker had been killed, and then searched the school.
The victims include three children aged 5, 8 and 11 and one teacher, Krantz said.
A seven-year-old child and a 54-year-old teacher were taken to a local hospital with "critical injuries", he added.
While police said the shooter was a local 16-year-old boy, they declined to add further details pending the ongoing investigation.
Police have not released the identities of any victims, the attacker, nor the bystander who shot him.
Schools throughout the city of Bend have been closed on Friday, with officials saying the community needs time to heal.
Around 450 children attend Silver Rail Elementary School, which has more than 40 adult staff members, police say.
Local media reports suggest the school received new doors in 2022 which can lock classrooms with a flip of a switch.
According to the K-12 School Shooting Database, there were 235 shooting incidents at American schools last year and at least 140 so far this year, including this one.