The police said they were able to speak to the suspect for about 30 minutes before the man became agitated while holding the boy tightly, reports Xinhua news agency.
One of the police officers was forced to open fire and shot the suspect dead to protect the boy.
"The officer felt and based on the subject's escalated actions to the child that it was necessary at that point to prevent that child from being severely injured or killed," a public information officer with the Kirkland Police Department, was quoted as saying.
The boy was safe but sent to a hospital for medical evaluation. The King County Sheriff's Department is investigating the incident.
This is the second officer-involved shooting incident in the Puget Sound region within one day.
Earlier, a Tacoma police officer shot and killed an armed man after he was trying to throw explosives at the Tacoma Northwest Detention Centre, a prison facility that holds immigrants in Washington.
Tacoma police said the man was attempting to set buildings on fire.